**Strain Measurements Relative to Normal State Enhance the Ability to Detect Non-Transmural Myocardial Infarction**

Noa Bachner-Hinenzon1,\*, Offir Ertracht2, 3,\*, Zvi Vered4,5, Marina Leitman4,5, Nir Zagury1, Ofer Binah2,3 and Dan Adam1 *1Faculty of Biomedical Engineering 2Department of Physiology 3Ruth and Bruce Rappaport Faculty of Medicine, Rappaport Family Institute for Research in the Medical Sciences Technion-Israel Institute of Technology, Haifa, 4Department of Cardiology, Assaf Harofeh Medical Center, Zerifin, 5Sackler School of Medicine Tel Aviv University Israel* 

#### **1. Introduction**

24 Echocardiography – New Techniques

Weidemann, F., Dommke, C., Bijnens, B., Claus, P., D'hooge, J., Mertens, P., Verbeken, E.,

Yip, G., Abraham, T., Belohlavek, M., Khandheria, B., Clinical Applications of Strain Rate

Yip, G., Khandheria, B., Belohlavek, M., Pislaru, C., Seward, J., Bailey, K., Tajik, A.J.,

Zwanenburg, J.J.M., Götte, M.J.W., Marcus, J.T., Kuijer, J.P.A., Knaapen, P., Heethaar, R.M.,

echocardiography. Eur Heart J, 2004; 25 (17):1517–1525.

Imaging, J Am Soc Echocardiogr, 2003; 16 (12): 1334-1342.

Imaging, Circulation, 2003; 107: 883-888.

Am Col Cardiol, 2004; 44:1664-1671.

for detecting regional inducible ischaemia during dobutamine stress

Maes, A., Van de Werf, F., De Scheerder, I., Sutherland, G.R., Defining the Transmurality of a Chronic Myocardial Infarction by Ultrasonic Strain-Rate

Pellikka, P., Abraham, T., Strain Echocardiography Tracks Dobutamine-Induced Decrease in Regional Myocardial Perfusion in Nonocclusive Coronary Stenosis, J

van Rossum, A.C., Propagation of Onset and Peak Time of Myocardial Shortening in Ischemic Versus Nonischemic Cardiomyopathy Assessment by Magnetic Resonance Imaging Myocardial Tagging, J Am Coll Cardiol 2005; 46: 2215–2222.

> Nowadays, diagnosis of heart pathologies in the clinic is mostly performed non-invasively by eyeballing the B-mode echocardiography cines and evaluating the ejection fraction and the regional wall motion. Yet, myocardial infarction (MI) usually causes reduced regional wall motion. During its diagnosis the echocardiographer grades the movement of each myocardial segment in order to estimate its function (Schiller et al., 1989). The disadvantage in this estimation is that it is subjective, and the echocardiographer must be experienced (Picano et al., 1991). As a result, echocardiographers provide different scoring to the same patient (Liel-Cohen et al., 2010). Hence, major efforts are invested in constructing automatic tools for wall motion estimation, as Speckle Tracking Echocardiography (STE).

> The STE is an angle-independent, cost-effective and available tool, developed for automatic evaluation of left ventricular (LV) regional function (Leitman et al., 2004, Liel-Cohen et al., 2010, Reisner et al., 2004). The STE program processes standard echocardiographic two dimensional (2D) gray-scale cine loops and tracks the speckle movement frame-by-frame (Rappaport et al., 2006). Consequently, the regional myocardial velocities are calculated and local strain parameters are provided. During MI, these local strain parameters, calculated in the longitudinal, circumferential and radial orientations, were found to be strongly correlated to MI size (Fu et al., 2009, Gjesdal et al., 2007, 2008, Migrino et al., 2007, 2008). Furthermore, the detection of large MI was found to be very reliable (Gjesdal et al., 2008, Migrino et al., 2007). Yet, the detection of small non-transmural MI requires improvement. Since it is important to achieve early detection of non-transmural MI, in the present study we investigated the

<sup>\*</sup> These authors contributed equally to the manuscript

Strain Measurements Relative to Normal State

level and the Papillary Muscles (PM) level.

**2.3 Speckle tracking echocardiography** 

value decreased to 7%, the relative value was -50%.

**2.4 Determination of MI size** 

Enhance the Ability to Detect Non-Transmural Myocardial Infarction 27

lightly sedated by an intraperitoneal injection of 29 mg/kg ketamine and 4.3 mg/kg xylazine mixture. Their chest was shaved and the scan was performed. During the scan, rats were placed in a left lateral decubitus position. The scan was performed via a commercially available echo-scanner - VividTM *i* ultrasound cardiovascular system (GE Healthcare Inc. Israel) using a 10S phased array pediatric transducer and a cardiac application. The transmission frequency was 10 MHz, the depth was 2.5 cm and the frame rate was 225-350 frames per second. The measurements included 2 short axis cross-sections at the Apical (AP)

The short axis ultrasound cines were post-processed by an enhanced STE program that measures the regional LV function at 6 segments with high spatial resolution (Bachner-Hinenzon et al., 2010, 2011). The program utilizes a commercial STE program called '2Dstrain' (EchoPAC Dimension '08, GE Healthcare Inc., Norway). The commercial program requests the user to mark the endocardial border and to choose the width of the myocardium, imposes a grid of points in the assigned region, and tracks the speckles near the points and evaluates their velocities at each frame (Rappaport et al., 2006). The myocardial velocities were not processed by the built-in smoothing of the commercial program, but were de-noised by a 3D wavelet representation (MATLAB software, MathWorks Inc. USA), thereby increasing the spatial resolution of the calculated functional measurements (Bachner-Hinenzon et al., 2010). Subsequently, the Radial Strain (SR) and Circumferential Strain (SC) were evaluated at 6 segments. The strain parameters were measured from the de-noised velocities of each point on the grid. The SR was calculated from the de-noised radial velocity, and the SC and LV rotation were calculated from the denoised circumferential velocity. Thereafter, the peak systolic values of the LV rotation SR and SC were calculated. The LV rotation is the rotation in degrees from the diastolic state. The SC and SR were measured in % from the diastolic state. End diastole is defined as the time just before the QRS complex in the ECG signal. The SC and SR were also calculated for each segment relatively to the normal values, as % of difference from the average baseline value divided by the average baseline value for each segment separately to create the 'SC rel' and 'SR rel'. For example, if the average normal strain was 14% at a specific segment, and the

The method used here for the assessment of the tissue viability, includes the use of two stains: (1) Evan's blue is used to delineate the Area At Risk (AAR), which is the area that was physically ligated 24 hours previously. (2) Triphenyltetrazolium Chloride (TTC), which delineates the MI area. Twenty four hrs post-surgery, the animals were re-anesthetized, intubated, and ventilated according to the protocol used in the surgery. The chest was opened to expose the heart. 1.5% Evan's blue solution (in PBS) was retrogradely injected through the aorta into the LV. The staining agent was then perfused through the open coronary arteries into the cardiac muscle, but not through the ligated artery and its downstream branches, delineating in dark blue the non-MI area of the heart. The heart was then removed and rinsed, in normal cold saline, of the excess Evan's blue and transferred to -80C for 5-6 min and sliced manually into 7 transverse slices. The slices were dipped in 1% TTC solution (in DDW pH=7.4)

hypothesis that taking into consideration the natural heterogeneity of the strain measurements among the different segments would enhance the differentiation between non-transmural MI and non-MI areas. This kind of measurement is particularly suitable for stressechocardiography since this prevalent clinical study includes comparison of the echo results at stress to those at baseline, and is specified for the detection of minor ischemia.

In this study 13 rats in the acute phase of MI (24 hours) and 8 sham operated rats were scanned, and their short axis cines were analyzed by a STE program. Subsequently, the Radial Strain (SR) and Circumferential Strain (SC) were evaluated at 6 myocardial segments. The first step was to decipher the natural heterogeneity at normal state by measuring the peak systolic strain values for each segment averaged over the 21 rats. The second step was to measure the segmental peak systolic strain values conventionally and relatively to normal state. Subsequently, the strain values were compared to the MI size and location.

#### **2. Methods**

Animal experiments were conducted according to the institutional animal ethical committee guidelines (ethics number: IL-101-10-2007) in 3 month old adult male Sprague-Dawley rats weighing 310-340 gr. Rats were maintained at the Experimental Surgical Unit of the Technion, and fed on normal rodent chow diet, with tap water ad libitum, according to the Technion guidelines for animal care. The rats were housed at a constant temperature (21°C) and relative humidity (60%) under a regular light/dark schedule (light 6:00 AM to 6:00 PM).

In this study 21 adult male Sprague-Dawley rats were investigated. Thirteen rats underwent myocardial ischemia and reperfusion surgery and 8 rats served as a corresponding sham group.

#### **2.1 Surgical procedure**

Male Sprague-Dawley rats were randomly divided into 2 groups. All rats were anesthetized with a combination of 87 mg/kg ketamine and 13 mg/kg xylazine mixture. The animals were intubated and mechanically ventilated using a Columbus Instruments small-animal mechanical respirator (Columbus Instruments 950 North Hague Av. Columbus, OH. USA) at a rate of 80-90 cycles per minute with a tidal volume of 1-2 ml/100 gr. Using a left thoracotomy, the chest was opened, the pericardial sac dissected, and the heart exposed. A single stitch was placed through the myocardium at a depth slightly greater than the perceived level of the left anterior descending artery (LAD) while taking care not to puncture the ventricular chamber (Bhindi et al., 2006, Hale et al., 2005). In the first group, which included 13 rats, the suture was tightened by a loop that allowed its rapid opening. Half an hour after the occlusion the suture was rapidly opened in order to resume blood flow through the LAD. In the second group, which included 8 rats, the thread was placed through the myocardium but it was not tied up; however, the chest remained opened for half an hour. Finally, the chest was closed and the animal was allowed to recover.

#### **2.2 Echocardiographic measurements**

Echocardiographic transthoratic scans were performed at baseline and at 24 hours of reperfusion. For the baseline and 24 hours post-MI echocardiographic scans, animals were lightly sedated by an intraperitoneal injection of 29 mg/kg ketamine and 4.3 mg/kg xylazine mixture. Their chest was shaved and the scan was performed. During the scan, rats were placed in a left lateral decubitus position. The scan was performed via a commercially available echo-scanner - VividTM *i* ultrasound cardiovascular system (GE Healthcare Inc. Israel) using a 10S phased array pediatric transducer and a cardiac application. The transmission frequency was 10 MHz, the depth was 2.5 cm and the frame rate was 225-350 frames per second. The measurements included 2 short axis cross-sections at the Apical (AP) level and the Papillary Muscles (PM) level.

#### **2.3 Speckle tracking echocardiography**

26 Echocardiography – New Techniques

hypothesis that taking into consideration the natural heterogeneity of the strain measurements among the different segments would enhance the differentiation between non-transmural MI and non-MI areas. This kind of measurement is particularly suitable for stressechocardiography since this prevalent clinical study includes comparison of the echo results at

In this study 13 rats in the acute phase of MI (24 hours) and 8 sham operated rats were scanned, and their short axis cines were analyzed by a STE program. Subsequently, the Radial Strain (SR) and Circumferential Strain (SC) were evaluated at 6 myocardial segments. The first step was to decipher the natural heterogeneity at normal state by measuring the peak systolic strain values for each segment averaged over the 21 rats. The second step was to measure the segmental peak systolic strain values conventionally and relatively to normal

Animal experiments were conducted according to the institutional animal ethical committee guidelines (ethics number: IL-101-10-2007) in 3 month old adult male Sprague-Dawley rats weighing 310-340 gr. Rats were maintained at the Experimental Surgical Unit of the Technion, and fed on normal rodent chow diet, with tap water ad libitum, according to the Technion guidelines for animal care. The rats were housed at a constant temperature (21°C) and relative humidity (60%) under a regular light/dark schedule (light 6:00 AM to 6:00 PM). In this study 21 adult male Sprague-Dawley rats were investigated. Thirteen rats underwent myocardial ischemia and reperfusion surgery and 8 rats served as a corresponding sham

Male Sprague-Dawley rats were randomly divided into 2 groups. All rats were anesthetized with a combination of 87 mg/kg ketamine and 13 mg/kg xylazine mixture. The animals were intubated and mechanically ventilated using a Columbus Instruments small-animal mechanical respirator (Columbus Instruments 950 North Hague Av. Columbus, OH. USA) at a rate of 80-90 cycles per minute with a tidal volume of 1-2 ml/100 gr. Using a left thoracotomy, the chest was opened, the pericardial sac dissected, and the heart exposed. A single stitch was placed through the myocardium at a depth slightly greater than the perceived level of the left anterior descending artery (LAD) while taking care not to puncture the ventricular chamber (Bhindi et al., 2006, Hale et al., 2005). In the first group, which included 13 rats, the suture was tightened by a loop that allowed its rapid opening. Half an hour after the occlusion the suture was rapidly opened in order to resume blood flow through the LAD. In the second group, which included 8 rats, the thread was placed through the myocardium but it was not tied up; however, the chest remained opened for

half an hour. Finally, the chest was closed and the animal was allowed to recover.

Echocardiographic transthoratic scans were performed at baseline and at 24 hours of reperfusion. For the baseline and 24 hours post-MI echocardiographic scans, animals were

stress to those at baseline, and is specified for the detection of minor ischemia.

state. Subsequently, the strain values were compared to the MI size and location.

**2. Methods** 

group.

**2.1 Surgical procedure** 

**2.2 Echocardiographic measurements** 

The short axis ultrasound cines were post-processed by an enhanced STE program that measures the regional LV function at 6 segments with high spatial resolution (Bachner-Hinenzon et al., 2010, 2011). The program utilizes a commercial STE program called '2Dstrain' (EchoPAC Dimension '08, GE Healthcare Inc., Norway). The commercial program requests the user to mark the endocardial border and to choose the width of the myocardium, imposes a grid of points in the assigned region, and tracks the speckles near the points and evaluates their velocities at each frame (Rappaport et al., 2006). The myocardial velocities were not processed by the built-in smoothing of the commercial program, but were de-noised by a 3D wavelet representation (MATLAB software, MathWorks Inc. USA), thereby increasing the spatial resolution of the calculated functional measurements (Bachner-Hinenzon et al., 2010). Subsequently, the Radial Strain (SR) and Circumferential Strain (SC) were evaluated at 6 segments. The strain parameters were measured from the de-noised velocities of each point on the grid. The SR was calculated from the de-noised radial velocity, and the SC and LV rotation were calculated from the denoised circumferential velocity. Thereafter, the peak systolic values of the LV rotation SR and SC were calculated. The LV rotation is the rotation in degrees from the diastolic state. The SC and SR were measured in % from the diastolic state. End diastole is defined as the time just before the QRS complex in the ECG signal. The SC and SR were also calculated for each segment relatively to the normal values, as % of difference from the average baseline value divided by the average baseline value for each segment separately to create the 'SC rel' and 'SR rel'. For example, if the average normal strain was 14% at a specific segment, and the value decreased to 7%, the relative value was -50%.

#### **2.4 Determination of MI size**

The method used here for the assessment of the tissue viability, includes the use of two stains: (1) Evan's blue is used to delineate the Area At Risk (AAR), which is the area that was physically ligated 24 hours previously. (2) Triphenyltetrazolium Chloride (TTC), which delineates the MI area. Twenty four hrs post-surgery, the animals were re-anesthetized, intubated, and ventilated according to the protocol used in the surgery. The chest was opened to expose the heart. 1.5% Evan's blue solution (in PBS) was retrogradely injected through the aorta into the LV. The staining agent was then perfused through the open coronary arteries into the cardiac muscle, but not through the ligated artery and its downstream branches, delineating in dark blue the non-MI area of the heart. The heart was then removed and rinsed, in normal cold saline, of the excess Evan's blue and transferred to -80C for 5-6 min and sliced manually into 7 transverse slices. The slices were dipped in 1% TTC solution (in DDW pH=7.4)

Strain Measurements Relative to Normal State

Enhance the Ability to Detect Non-Transmural Myocardial Infarction 29

systolic values at the AP level is significant (P<0.001), while this heterogeneity is no longer significant at the PM level (P=0.06, N.S). Yet, it can be seen that the pattern of the peak systolic SC lines in Fig. 1B are similar for the AP and PM levels. One way ANOVA test for the peak systolic SR values demonstrate that the heterogeneity of the peak systolic SR is significant at both AP and PM levels (P<0.001). Both AP and PM levels show lower SR at the inferior septum

and anterior septum, and the values are higher for the lateral wall (P<0.05).

1B. 1C.

Fig. 1. The heterogeneity of normal strain values in % from diastolic state. Typical maps of end-systolic circumferential (SC) and radial (SR) strains at the apical (AP) and papillary muscles (PM) levels (1A). Blue color is defined as negative and red as positive. Peak systolic SC (1B) and SR (1C) at the different segments of the AP and PM levels averaged over 21 rats.

at 37C for 20 min, and then rinsed in PBS of the excess TTC solution, and weighted (Ojha et al., 2008, Reinhardt et al., 1993). To improve the delineation of the different colours, the slices were kept at 4C in PBS + sodium azide (0.01%), as preservative, for 3 weeks (Pitts et al., 2007). Subsequently, the slices were placed on top of a light table and photographed on both sides. Using the ImageJ software (NIH, Bethesda, MD, USA http://rsb.info.nih.gov/ij) the pictures were analyzed, and the different areas were delineated. Using the weights of the slices and the percentages of the different colored areas of each slice, we calculated the percent of non-MI cardiac muscle (dark blue), area at risk (red and white) and infarcted area (white). The slices were numbered from 1 to 7 from apex to atria. The slices that matched the AP and PM levels of short axis scans were slices number 3 and 4, respectively. These slices were divided to 6 equal radial segments: inferior septum, anterior septum, anterior wall, lateral wall, posterior wall and inferior wall. Each segment was classified as normal or damaged with transmural or nontransmural MI, according to the TTC stain.

#### **2.5 Statistical analysis**

All variables were expressed by the mean ± SEM. Paired t-test was performed in order to compare the MI size at the AP and PM levels. One-way analysis of variance (ANOVA) for unequal variance was used to compare MI size (normal/transmural/non-transmural) to the peak systolic strains (SC, SR, SC rel, SR rel). One-way ANOVA for unequal variance was also used in order to compare between the peak systolic strain of the different segments for the baseline and 24 hours of reperfusion results. Two-way repeated measures ANOVA was used to compare the peak systolic strains (SC, SR) at different time points for the MI and sham groups. Receiver operating characteristics (ROC) method was used in order to predict transmural MI from all other segments (normal and non-transmural). The ROC method was also used in order to predict non-transmural MI from the normal segments. The area under the ROC curves was measured and compared in order to test whether the difference between the ROC curves was significant.

#### **3. Results**

#### **3.1 MI size**

In 156 segments of the AP and PM levels of the 13 MI rats the determination of MI size by the TTC staining yielded the following results: 91 normal segments, 22 non-transmural MI and 43 transmural MI segments. The transmural MI occurred mostly at the anterior and lateral walls (in 10 out of 13 rats), while non-transmural MIs were visualized at the posterior and inferior walls (in 9 out of 13 rats). The total MI size at the AP level was 23±13 % (min 0%, max 47%), and at the PM level was 19±8 % (min 7%, max 34%), while there was no significant difference in the MI size between the two levels. The results for the sham group showed 86 normal segments for the 8 sham rats.

#### **3.2 Strain measurements at baseline**

Heterogeneity of the peak systolic strains was defined as a significant difference between the measured values at the different segments. Typical strain maps at the normal state, which are presented in Fig. 1A, illustrate the heterogeneity of the SR and SC. The average baseline values of SC and SR for 21 rats are presented in Fig. 1B and Fig. 1C, respectively. One way ANOVA test for the normal peak systolic SC values demonstrate that the heterogeneity of the peak

at 37C for 20 min, and then rinsed in PBS of the excess TTC solution, and weighted (Ojha et al., 2008, Reinhardt et al., 1993). To improve the delineation of the different colours, the slices were kept at 4C in PBS + sodium azide (0.01%), as preservative, for 3 weeks (Pitts et al., 2007). Subsequently, the slices were placed on top of a light table and photographed on both sides. Using the ImageJ software (NIH, Bethesda, MD, USA http://rsb.info.nih.gov/ij) the pictures were analyzed, and the different areas were delineated. Using the weights of the slices and the percentages of the different colored areas of each slice, we calculated the percent of non-MI cardiac muscle (dark blue), area at risk (red and white) and infarcted area (white). The slices were numbered from 1 to 7 from apex to atria. The slices that matched the AP and PM levels of short axis scans were slices number 3 and 4, respectively. These slices were divided to 6 equal radial segments: inferior septum, anterior septum, anterior wall, lateral wall, posterior wall and inferior wall. Each segment was classified as normal or damaged with transmural or non-

All variables were expressed by the mean ± SEM. Paired t-test was performed in order to compare the MI size at the AP and PM levels. One-way analysis of variance (ANOVA) for unequal variance was used to compare MI size (normal/transmural/non-transmural) to the peak systolic strains (SC, SR, SC rel, SR rel). One-way ANOVA for unequal variance was also used in order to compare between the peak systolic strain of the different segments for the baseline and 24 hours of reperfusion results. Two-way repeated measures ANOVA was used to compare the peak systolic strains (SC, SR) at different time points for the MI and sham groups. Receiver operating characteristics (ROC) method was used in order to predict transmural MI from all other segments (normal and non-transmural). The ROC method was also used in order to predict non-transmural MI from the normal segments. The area under the ROC curves was measured and compared in order to test whether the difference

In 156 segments of the AP and PM levels of the 13 MI rats the determination of MI size by the TTC staining yielded the following results: 91 normal segments, 22 non-transmural MI and 43 transmural MI segments. The transmural MI occurred mostly at the anterior and lateral walls (in 10 out of 13 rats), while non-transmural MIs were visualized at the posterior and inferior walls (in 9 out of 13 rats). The total MI size at the AP level was 23±13 % (min 0%, max 47%), and at the PM level was 19±8 % (min 7%, max 34%), while there was no significant difference in the MI size between the two levels. The results for the sham group

Heterogeneity of the peak systolic strains was defined as a significant difference between the measured values at the different segments. Typical strain maps at the normal state, which are presented in Fig. 1A, illustrate the heterogeneity of the SR and SC. The average baseline values of SC and SR for 21 rats are presented in Fig. 1B and Fig. 1C, respectively. One way ANOVA test for the normal peak systolic SC values demonstrate that the heterogeneity of the peak

transmural MI, according to the TTC stain.

between the ROC curves was significant.

showed 86 normal segments for the 8 sham rats.

**3.2 Strain measurements at baseline** 

**2.5 Statistical analysis** 

**3. Results 3.1 MI size** 

systolic values at the AP level is significant (P<0.001), while this heterogeneity is no longer significant at the PM level (P=0.06, N.S). Yet, it can be seen that the pattern of the peak systolic SC lines in Fig. 1B are similar for the AP and PM levels. One way ANOVA test for the peak systolic SR values demonstrate that the heterogeneity of the peak systolic SR is significant at both AP and PM levels (P<0.001). Both AP and PM levels show lower SR at the inferior septum and anterior septum, and the values are higher for the lateral wall (P<0.05).

Fig. 1. The heterogeneity of normal strain values in % from diastolic state. Typical maps of end-systolic circumferential (SC) and radial (SR) strains at the apical (AP) and papillary muscles (PM) levels (1A). Blue color is defined as negative and red as positive. Peak systolic SC (1B) and SR (1C) at the different segments of the AP and PM levels averaged over 21 rats.

Strain Measurements Relative to Normal State

posterior and inferior walls (Fig. 3D , P<0.01).

Enhance the Ability to Detect Non-Transmural Myocardial Infarction 31

The values of peak systolic SR for the MI rats at the AP level at the anterior and lateral walls were smaller at 24 hours of reperfusion than baseline (Fig. 3B, P<0.001); however, the same reduction was noticed at the anterior wall of the sham group (Fig. 3B). Thus, only the peak systolic SR of the lateral wall was significantly lower for the MI rats (P<0.05). At the PM level no significant difference was found in the peak systolic SR between the sham group and the MI group (Fig. 3D). In both groups the peak systolic SR became smaller at the lateral,

In both MI and sham groups, the LV rotation was depressed after surgery. Ten minutes after reperfusion, the LV apical rotations of the MI and sham groups were 0.2±0.4 deg and - 1.1±1.4 deg, respectively. Twenty four hours after reperfusion, the LV rotations at the AP

level of the MI and sham groups were 0.0±0.5 deg and -0.3±0.6 deg, respectively.

Fig. 3. Segmental circumferential strain (SC) at the apical and papillary muscles levels as function of time (baseline and 24 hours of reperfusion) for the MI group and for the sham group (3A, 3C). Segmental radial strain (SR) at the apical and papillary muscles levels as

Linear regression was performed between the MI size and the peak systolic SC and SR for both AP and PM levels. The linear regression was performed between the size of the MI (as % of area from the total area of the cross-section) and the peak systolic SC and SR averaged over the anterior, lateral and posterior segments of the same cross-section (MI area). Subsequently, the linear regression was performed between the cross-sectional MI size and

function of time for the MI group and for the sham group (3B, 3D).

**3.5 Strain measurements versus MI size** 

The global LV rotation was 4.9±0.5 deg counterclockwise at the AP level and 1.6±0.6 deg counterclockwise at the PM level.

#### **3.3 Segmental strain measurements as function of time post-MI**

Examples of strain maps of peak systolic values of SC and SR are depicted in Fig. 2 for slices of sham, non-transmural MI, and transmural MI. The changes in peak systolic SC and SR of both MI and sham groups at baseline and 24 hours of reperfusion are demonstrated in Fig. 3A-D. Twenty four hours after reperfusion, the peak systolic SC and SR were significantly decreased at the free wall in both AP and PM levels (Figs. 3A-D, P<0.05), while the septum maintained normal values.

Fig. 2. Examples of TTC staining and end-systolic strain maps (% from diastolic state) for sham, non-transmural MI and transmural MI rats. Blue color is defined as negative and red as positive. In the example of sham rat it is well seen that the papillary muscles (PM) level is injured even though there was no LAD occlusion. In the non-transmural example, the yellow positive SC is the MI area. This area looks rather normal in the SR map. In the transmural example, green color of SC is zero, and light blue of SR is the thinning of the myocardium.

#### **3.4 Strain measurements of MI rats versus sham rats**

The peak systolic SC values of the MI group decreased from normal values at the free wall of the AP and PM levels (Fig. 3A, 3C ,P<0.05). However, the peak systolic SC values of the sham group decreased only at the lateral wall of the AP level (Fig. 3A, P<0.05), and posterior wall of the PM level (Fig. 3C, P<0.01), while there was no significant difference in the peak systolic SC values between the MI and sham rats in these segments. The peak systolic SC at the PM level maintained normal values for the sham group except for a slight reduction at the posterior wall (Fig. 3C, P<0.01).

The global LV rotation was 4.9±0.5 deg counterclockwise at the AP level and 1.6±0.6 deg

Examples of strain maps of peak systolic values of SC and SR are depicted in Fig. 2 for slices of sham, non-transmural MI, and transmural MI. The changes in peak systolic SC and SR of both MI and sham groups at baseline and 24 hours of reperfusion are demonstrated in Fig. 3A-D. Twenty four hours after reperfusion, the peak systolic SC and SR were significantly decreased at the free wall in both AP and PM levels (Figs. 3A-D, P<0.05), while the septum

Fig. 2. Examples of TTC staining and end-systolic strain maps (% from diastolic state) for sham, non-transmural MI and transmural MI rats. Blue color is defined as negative and red as positive. In the example of sham rat it is well seen that the papillary muscles (PM) level is injured even though there was no LAD occlusion. In the non-transmural example, the yellow positive SC is the MI area. This area looks rather normal in the SR map. In the transmural example, green color of SC is zero, and light blue of SR is the thinning of the myocardium.

The peak systolic SC values of the MI group decreased from normal values at the free wall of the AP and PM levels (Fig. 3A, 3C ,P<0.05). However, the peak systolic SC values of the sham group decreased only at the lateral wall of the AP level (Fig. 3A, P<0.05), and posterior wall of the PM level (Fig. 3C, P<0.01), while there was no significant difference in the peak systolic SC values between the MI and sham rats in these segments. The peak systolic SC at the PM level maintained normal values for the sham group except for a slight reduction at

**3.4 Strain measurements of MI rats versus sham rats** 

the posterior wall (Fig. 3C, P<0.01).

**3.3 Segmental strain measurements as function of time post-MI** 

counterclockwise at the PM level.

maintained normal values.

The values of peak systolic SR for the MI rats at the AP level at the anterior and lateral walls were smaller at 24 hours of reperfusion than baseline (Fig. 3B, P<0.001); however, the same reduction was noticed at the anterior wall of the sham group (Fig. 3B). Thus, only the peak systolic SR of the lateral wall was significantly lower for the MI rats (P<0.05). At the PM level no significant difference was found in the peak systolic SR between the sham group and the MI group (Fig. 3D). In both groups the peak systolic SR became smaller at the lateral, posterior and inferior walls (Fig. 3D , P<0.01).

In both MI and sham groups, the LV rotation was depressed after surgery. Ten minutes after reperfusion, the LV apical rotations of the MI and sham groups were 0.2±0.4 deg and - 1.1±1.4 deg, respectively. Twenty four hours after reperfusion, the LV rotations at the AP level of the MI and sham groups were 0.0±0.5 deg and -0.3±0.6 deg, respectively.

Fig. 3. Segmental circumferential strain (SC) at the apical and papillary muscles levels as function of time (baseline and 24 hours of reperfusion) for the MI group and for the sham group (3A, 3C). Segmental radial strain (SR) at the apical and papillary muscles levels as function of time for the MI group and for the sham group (3B, 3D).

#### **3.5 Strain measurements versus MI size**

Linear regression was performed between the MI size and the peak systolic SC and SR for both AP and PM levels. The linear regression was performed between the size of the MI (as % of area from the total area of the cross-section) and the peak systolic SC and SR averaged over the anterior, lateral and posterior segments of the same cross-section (MI area). Subsequently, the linear regression was performed between the cross-sectional MI size and

Strain Measurements Relative to Normal State

Enhance the Ability to Detect Non-Transmural Myocardial Infarction 33

PM P<0.001). However, it was possible to do so with SR values only at the PM level, as seen in Fig. 5F (P<0.01). The non-transmural MI segments could be distinguished from the normal segments at the PM level only by using peak systolic SC values as seen in Fig. 5E (P<0.001), and not by using peak systolic SR values (Fig. 5F). At the AP level it was impossible to distinguish the non-transmural MI segments from the normal segments by

Fig. 5. Apical peak systolic circumferential (SC, 5A ) and radial (SR, 5B) strains versus MI size (normal, transmural and non-transmural). Apical peak systolic circumferential (SC rel, 5C)

circumferential (SC, 5E ) and radial (SR, 5F) strains at the papillary muscles level versus MI size. Peak systolic circumferential (SC rel, 5G ) and radial (SR rel, 5H) strains relative to normal state at the papillary muscles level versus MI size. \*P<0.01, \*\*P<0.001, †P<0.05.

and radial (SR rel, 5D) strains relative to normal state versus MI size. Peak systolic

using peak systolic SC and SR as seen in Figs. 5A and 5B, respectively.

the peak systolic SC and SR averaged over the inferior septum, anterior septum and inferior wall (non-MI area). This analysis revealed high correlation between the MI size and the peak systolic strains of the MI area (Fig. 4). The correlation was higher at the AP level (SC R2=0.89, SR R2=0.73) than at the PM level (SC R2=0.73, SR R2=0.67) as seen in Fig. 4. In contrast, no correlation was found between the peak systolic SC and SR of the non-MI area and the MI size (AP: SC R2=0.25, SR R2=0.02, PM: SC R2=0.00, SR R2=0.05) (data not shown). Finally, there was no correlation between the peak systolic SC and SR of the MI area and the non-MI area (AP: SC R2=0.27, SR R2=0.06, PM: SC R2=0.24, SR R2=0.06); see discussion.

Fig. 4. Scatter plot and linear regression of apical peak systolic circumferential (SC, 4A) and radial (SR, 4B) strains versus MI size. Scatter plot and linear regression of peak systolic circumferential (SC, 4C) and radial (SR, 4D) strains at the papillary muscles level versus MI size. The strains are averaged over the anterior, lateral and posterior walls, and the MI size is measured per level.

Next, statistical analysis was performed to see whether there is a significant difference between the strain measurements of normal, non-transmural and transmural MI. As expected, segments with transmural MI demonstrated significantly lower peak systolic strain values than the normal segments in both AP and PM levels (Fig. 5, P<0.001). Furthermore, the segments with transmural MI could be distinguished from non-transmural MI segments by utilizing peak systolic SC values as seen in Fig. 5A and Fig. 5E (AP P<0.01,

the peak systolic SC and SR averaged over the inferior septum, anterior septum and inferior wall (non-MI area). This analysis revealed high correlation between the MI size and the peak systolic strains of the MI area (Fig. 4). The correlation was higher at the AP level (SC R2=0.89, SR R2=0.73) than at the PM level (SC R2=0.73, SR R2=0.67) as seen in Fig. 4. In contrast, no correlation was found between the peak systolic SC and SR of the non-MI area and the MI size (AP: SC R2=0.25, SR R2=0.02, PM: SC R2=0.00, SR R2=0.05) (data not shown). Finally, there was no correlation between the peak systolic SC and SR of the MI area and the non-MI

Fig. 4. Scatter plot and linear regression of apical peak systolic circumferential (SC, 4A) and radial (SR, 4B) strains versus MI size. Scatter plot and linear regression of peak systolic circumferential (SC, 4C) and radial (SR, 4D) strains at the papillary muscles level versus MI size. The strains are averaged over the anterior, lateral and posterior walls, and the MI size

Next, statistical analysis was performed to see whether there is a significant difference between the strain measurements of normal, non-transmural and transmural MI. As expected, segments with transmural MI demonstrated significantly lower peak systolic strain values than the normal segments in both AP and PM levels (Fig. 5, P<0.001). Furthermore, the segments with transmural MI could be distinguished from non-transmural MI segments by utilizing peak systolic SC values as seen in Fig. 5A and Fig. 5E (AP P<0.01,

is measured per level.

area (AP: SC R2=0.27, SR R2=0.06, PM: SC R2=0.24, SR R2=0.06); see discussion.

PM P<0.001). However, it was possible to do so with SR values only at the PM level, as seen in Fig. 5F (P<0.01). The non-transmural MI segments could be distinguished from the normal segments at the PM level only by using peak systolic SC values as seen in Fig. 5E (P<0.001), and not by using peak systolic SR values (Fig. 5F). At the AP level it was impossible to distinguish the non-transmural MI segments from the normal segments by using peak systolic SC and SR as seen in Figs. 5A and 5B, respectively.

Fig. 5. Apical peak systolic circumferential (SC, 5A ) and radial (SR, 5B) strains versus MI size (normal, transmural and non-transmural). Apical peak systolic circumferential (SC rel, 5C) and radial (SR rel, 5D) strains relative to normal state versus MI size. Peak systolic circumferential (SC, 5E ) and radial (SR, 5F) strains at the papillary muscles level versus MI size. Peak systolic circumferential (SC rel, 5G ) and radial (SR rel, 5H) strains relative to normal state at the papillary muscles level versus MI size. \*P<0.01, \*\*P<0.001, †P<0.05.

Strain Measurements Relative to Normal State

A

B

Enhance the Ability to Detect Non-Transmural Myocardial Infarction 35

Fig. 6. Receiver operating characteristics curve of apical circumferential (SC) and radial (SR) strains and apical circumferential and radial strains relative to normal state (SC rel, SR rel) in the detection of transmural MI (6A) and non-transmural MI (6B). In the detection of nontransmural MI there is a significant difference between the SC and SR curves and the SC rel

and SR rel curves (P<0.01).

#### **3.6 Strain measurements relative to normal state values**

The peak systolic SC and SR relative to normal state values distinguished non-transmural MI from normal segments at the AP (Fig. 5C and Fig. 5D) and PM (Fig. 5G and Fig. 5H) levels (SC rel P=0.01, SR rel P<0.05, PM: SC rel P<0.001, SR rel P<0.001), while it was impossible at the AP level (Figs. 5A and 5B), and was possible at the PM level only by peak systolic SC (Fig. 5E).

In order to compare between the peak systolic SC and SR and their values relative to normal state (peak systolic SC rel and SR rel) a ROC method was utilized and the areas under the curves were compared (Fig 6). The results are summarized in Table 1. In all cases the SC relative to its normal state values provided the best results; however, in the detection of transmural MI, there is no significant difference between SC relative to normal state and peak systolic SC. The comparison between ROC curves, analyzing the detection of transmural MI at the AP level, appears in Fig. 6A. When studying the capabilities of detecting non-transmural MI, the SC relative to its normal state values provided better results at the apex as seen in Fig. 6B (P<0.01), however, there was no significant difference in the capability of detection at the PM level. The detection of non-transmural MI by peak systolic SR was enhanced by utilizing the measurement of peak systolic SR relative to its normal state in both AP and PM levels. Nevertheless, at the PM level this detection was significantly less effective than the detection by peak systolic SC as seen in Table 1 (P<0.05).


SC and SR are the peak systolic values. SC rel and SR rel are the peak systolic values relative to normal state. Specificity and sensitivity values appear on the left and their cut-off value appears on the right. Significant difference of ROC curves between the parameter and the parameter relative to normal state appears in the table as \*P<0.01, † P<0.05.

Table 1. Specificity and sensitivity of peak systolic SC and SR

The peak systolic SC and SR relative to normal state values distinguished non-transmural MI from normal segments at the AP (Fig. 5C and Fig. 5D) and PM (Fig. 5G and Fig. 5H) levels (SC rel P=0.01, SR rel P<0.05, PM: SC rel P<0.001, SR rel P<0.001), while it was impossible at the AP level (Figs. 5A and 5B), and was possible at the PM level only by peak systolic SC

In order to compare between the peak systolic SC and SR and their values relative to normal state (peak systolic SC rel and SR rel) a ROC method was utilized and the areas under the curves were compared (Fig 6). The results are summarized in Table 1. In all cases the SC relative to its normal state values provided the best results; however, in the detection of transmural MI, there is no significant difference between SC relative to normal state and peak systolic SC. The comparison between ROC curves, analyzing the detection of transmural MI at the AP level, appears in Fig. 6A. When studying the capabilities of detecting non-transmural MI, the SC relative to its normal state values provided better results at the apex as seen in Fig. 6B (P<0.01), however, there was no significant difference in the capability of detection at the PM level. The detection of non-transmural MI by peak systolic SR was enhanced by utilizing the measurement of peak systolic SR relative to its normal state in both AP and PM levels. Nevertheless, at the PM level this detection was significantly less effective than the detection by peak systolic SC as seen in Table 1

Transmural MI Non-transmural MI

Sensitivity 96 %, -7.5 % 100%, -9.4% 88%, -13.4% 100%, -13.4% Specificity 90%, -7.5 % 80%, -9.4% 65%, -13.4% 84%, -13.4%

Sensitivity 84%, 7.7% 81%, 7.5% 100%, 11.1% 57%, 10.3% Specificity 80%, 7.7% 98%, 7.5% 72%, 11.1% 89%, 10.3%

Specificity **96%, -68.5% 83%, -56.9% 84%, -50.7%, \* 87%, -41.1%** 

Sensitivity 77%, -77.3%, † 82%, -77.3% 100%, -58.1%, **\*** 64%, -48.5%,

Specificity 92%, -77.3%, † 97%, -77.3% 81%, -58.1%, **\*** 84%, -48.5%,

†

†

SC rel Sensitivity **100%, -68.5% 100%, -56.9% 88%, -50.7%, \* 100%, -41.1%** 

SC and SR are the peak systolic values. SC rel and SR rel are the peak systolic values relative to normal state. Specificity and sensitivity values appear on the left and their cut-off value appears on the right. Significant difference of ROC curves between the parameter and the parameter relative to normal state

Parameter AP PM AP PM

**3.6 Strain measurements relative to normal state values** 

(Fig. 5E).

(P<0.05).

SC

SR

SR rel

appears in the table as \*P<0.01, † P<0.05.

Table 1. Specificity and sensitivity of peak systolic SC and SR

Fig. 6. Receiver operating characteristics curve of apical circumferential (SC) and radial (SR) strains and apical circumferential and radial strains relative to normal state (SC rel, SR rel) in the detection of transmural MI (6A) and non-transmural MI (6B). In the detection of nontransmural MI there is a significant difference between the SC and SR curves and the SC rel and SR rel curves (P<0.01).

Strain Measurements Relative to Normal State

contractility (Vartdal et al., 2007).

**4.1 Study limitations** 

image quality.

**5. Conclusions** 

measurement peak systolic SC values of the AP level.

Enhance the Ability to Detect Non-Transmural Myocardial Infarction 37

classified by mistake as an infarcted area. It is important to note that taking into consideration the heterogeneity of the normal values is relevant only if the heterogeneity is significant. The heterogeneity of the peak systolic SC at the PM level is not statistically significant. Thus, taking into consideration the normal values influences only the

The detection of transmural MI does not require normalization to baseline. The strain values are severely reduced, and in some cases the myocardium even undergoes stretching instead of contraction during diastole, as seen in the transmural MI example in Fig. 2 and in the study of Migrino et al. (Migrino et al., 2007). In this study we found that the peak systolic SC is a better detector of transmural MI than peak systolic SR (P<0.05). Gjesdal et al. (Gjesdal et al., 2008)and Popović et al. (Popović et al., 2007) ) also reported better detection of transmural MI by SC than by SR (Gjesdal et al., 2008); however Migrino et al. reported that SR is a better predictor of transmural MI (Migrino et al., 2007, 2008). The SR cannot be a better predictor of transmural MI since the STE commercial program contains stronger spatial smoothing at the radial direction than that at the circumferential direction. This phenomenon is demonstrated by comparing Figs. 2B and 2C in Popović et al. In their Fig. 2B there was heterogeneity in the segmental peak systolic SC in normal and MI states. In contrast, no heterogeneity was seen by the SR in Fig. 2C (Popović et al., 2007). The normal heterogeneity of the peak systolic SR that was measured in our present study (Fig. 1C) can be seen by eyeballing the short-axis scans. Another influence of the smoothing process is the correlation between the strain at the MI areas and the non-MI areas. Migrino et al. reported a correlation of 0.82 between end systolic SR of the MI and periinfarct areas. Moreover, they reported a correlation of 0.64 between end systolic SR of the MI and remote areas (Migrino et al., 2008). These strong correlations, which occur due to the smoothing process of the commercial program, do not occur when using the wavelet de-noising process that we propose in this study. The correlation between the non-MI area and the MI area in this study was 0.24 for the SC and 0.06 for the SR at the PM level. This result demonstrates that the peak systolic SR of the remote areas at 24 hours of reperfusion do not correlate to the MI size. This result was not surprising since a previous Doppler echocardiography study has already reported that remote areas can show normal

The main limitation of the wavelet de-noising process used here is its sensitivity to artifacts at the B-mode cines. The commercial program compensates for artifacts, such as areas in which the myocardium is shaded by the ribs (black area), by imposing there the averaged values. The wavelet de-noising shows no movement in these areas while the commercial program depicts normal movement. Thus, when applying the wavelet denoising algorithm used here, it is important to include only ultrasound cines with good

Based on our results we concluded that in the rat model a natural heterogeneity among the strain values exists. Taking into consideration this normal heterogeneity, by measuring the

#### **4. Discussion**

In the present study we tested the hypothesis that taking into consideration the natural heterogeneity of the strain measurements among the different segments would enhance the differentiation between non-transmural MI and non-MI areas. Our main findings were: 1) In normal rats, while peak systolic SC is heterogeneous at the AP level, the heterogeneity is not statistically significant at the PM level. 2) In normal rats, peak systolic SR is heterogeneous at both AP and PM short axis levels. 3) Peak systolic SC is more sensitive to the presence of MI than peak systolic SR. 4) Peak systolic SC value, when calculated relatively to normal values (% of reduction from normal value) is more sensitive to the presence of non-transmural MI than the conventional peak systolic SC value. 5) Peak systolic strains (SC and SR) at the MI areas have high correlation to MI size. 6) Peak systolic strains (SC and SR) at remote areas from the MI do not correlate to MI size. 7) Sham operated rats demonstrated lower strain values mostly at the anterior and lateral walls probably due to stunning of the myocardium due to the insertion of the needle (The needle was inserted and the thread was placed through the myocardium but it was not tied up). 8) LV apical rotation was severely depressed in both MI and sham rats.

In this study the heterogeneity of the peak systolic SC and SR was demonstrated in normal rats. Moreover, it was shown that this heterogeneity should be taken into account when attempting to detect non-transmural MI. When the normal heterogeneity of the strain values was not taken into consideration, normal segments with lower strain values were classified as non-transmural MI (false positive), and thus the specificity of the classification of non-transmural MI was only 65% and 69%, when using peak systolic SC and SR, respectively (Table 1). Measuring the peak systolic SC and SR values relatively to normal values caused an increase of the correct classification of the non-transmural MI, and the specificity was increased to 84% and 79%, when using peak systolic SC and SR relative to normal values, respectively. It is important to mention that the peak systolic strain for each segment was measured relatively to the average normal value of 21 rats and not relatively to its own baseline value, which may allow a more general implementation of the technique. Such a sensitive regional analysis of the strain measurements was possible due to the utilization of a novel wavelet de-noising process, which was applied to the myocardial velocities after the speckle tracking, instead of the built-in smoothing process of the commercial STE program.

Detection of MI by STE was previously reported by Gjesdal et al., who analyzed the global longitudinal and circumferential strains of patients with chronic ischemic heart disease (Gjesdal et al., 2007, 2008). The detection of MI mass was found to be precise when by utilizing global longitudinal and circumferential strains (Gjesdal et al., 2008). However, in the present study, we propose to enhance the detection, specifically of non-transmural MI, by taking into consideration the normal segmental heterogeneity. The normal segmental heterogeneity of the longitudinal strain was studied by Marwick et al., who performed the measurements over 250 normal subjects (Marwick et al., 2009). Marwick et al. found peak systolic longitudinal strain of -13.7±4.0 % at the basal septum, while the global longitudinal strain value of -15.3±1.9% was considered by Gjesdal et al. as a value signifying a medium sized MI. Thus, normal segments with lower strain values might be

In the present study we tested the hypothesis that taking into consideration the natural heterogeneity of the strain measurements among the different segments would enhance the differentiation between non-transmural MI and non-MI areas. Our main findings were: 1) In normal rats, while peak systolic SC is heterogeneous at the AP level, the heterogeneity is not statistically significant at the PM level. 2) In normal rats, peak systolic SR is heterogeneous at both AP and PM short axis levels. 3) Peak systolic SC is more sensitive to the presence of MI than peak systolic SR. 4) Peak systolic SC value, when calculated relatively to normal values (% of reduction from normal value) is more sensitive to the presence of non-transmural MI than the conventional peak systolic SC value. 5) Peak systolic strains (SC and SR) at the MI areas have high correlation to MI size. 6) Peak systolic strains (SC and SR) at remote areas from the MI do not correlate to MI size. 7) Sham operated rats demonstrated lower strain values mostly at the anterior and lateral walls probably due to stunning of the myocardium due to the insertion of the needle (The needle was inserted and the thread was placed through the myocardium but it was not tied up). 8) LV apical rotation was severely

In this study the heterogeneity of the peak systolic SC and SR was demonstrated in normal rats. Moreover, it was shown that this heterogeneity should be taken into account when attempting to detect non-transmural MI. When the normal heterogeneity of the strain values was not taken into consideration, normal segments with lower strain values were classified as non-transmural MI (false positive), and thus the specificity of the classification of non-transmural MI was only 65% and 69%, when using peak systolic SC and SR, respectively (Table 1). Measuring the peak systolic SC and SR values relatively to normal values caused an increase of the correct classification of the non-transmural MI, and the specificity was increased to 84% and 79%, when using peak systolic SC and SR relative to normal values, respectively. It is important to mention that the peak systolic strain for each segment was measured relatively to the average normal value of 21 rats and not relatively to its own baseline value, which may allow a more general implementation of the technique. Such a sensitive regional analysis of the strain measurements was possible due to the utilization of a novel wavelet de-noising process, which was applied to the myocardial velocities after the speckle tracking, instead of the

Detection of MI by STE was previously reported by Gjesdal et al., who analyzed the global longitudinal and circumferential strains of patients with chronic ischemic heart disease (Gjesdal et al., 2007, 2008). The detection of MI mass was found to be precise when by utilizing global longitudinal and circumferential strains (Gjesdal et al., 2008). However, in the present study, we propose to enhance the detection, specifically of non-transmural MI, by taking into consideration the normal segmental heterogeneity. The normal segmental heterogeneity of the longitudinal strain was studied by Marwick et al., who performed the measurements over 250 normal subjects (Marwick et al., 2009). Marwick et al. found peak systolic longitudinal strain of -13.7±4.0 % at the basal septum, while the global longitudinal strain value of -15.3±1.9% was considered by Gjesdal et al. as a value signifying a medium sized MI. Thus, normal segments with lower strain values might be

**4. Discussion**

depressed in both MI and sham rats.

built-in smoothing process of the commercial STE program.

classified by mistake as an infarcted area. It is important to note that taking into consideration the heterogeneity of the normal values is relevant only if the heterogeneity is significant. The heterogeneity of the peak systolic SC at the PM level is not statistically significant. Thus, taking into consideration the normal values influences only the measurement peak systolic SC values of the AP level.

The detection of transmural MI does not require normalization to baseline. The strain values are severely reduced, and in some cases the myocardium even undergoes stretching instead of contraction during diastole, as seen in the transmural MI example in Fig. 2 and in the study of Migrino et al. (Migrino et al., 2007). In this study we found that the peak systolic SC is a better detector of transmural MI than peak systolic SR (P<0.05). Gjesdal et al. (Gjesdal et al., 2008)and Popović et al. (Popović et al., 2007) ) also reported better detection of transmural MI by SC than by SR (Gjesdal et al., 2008); however Migrino et al. reported that SR is a better predictor of transmural MI (Migrino et al., 2007, 2008). The SR cannot be a better predictor of transmural MI since the STE commercial program contains stronger spatial smoothing at the radial direction than that at the circumferential direction. This phenomenon is demonstrated by comparing Figs. 2B and 2C in Popović et al. In their Fig. 2B there was heterogeneity in the segmental peak systolic SC in normal and MI states. In contrast, no heterogeneity was seen by the SR in Fig. 2C (Popović et al., 2007). The normal heterogeneity of the peak systolic SR that was measured in our present study (Fig. 1C) can be seen by eyeballing the short-axis scans. Another influence of the smoothing process is the correlation between the strain at the MI areas and the non-MI areas. Migrino et al. reported a correlation of 0.82 between end systolic SR of the MI and periinfarct areas. Moreover, they reported a correlation of 0.64 between end systolic SR of the MI and remote areas (Migrino et al., 2008). These strong correlations, which occur due to the smoothing process of the commercial program, do not occur when using the wavelet de-noising process that we propose in this study. The correlation between the non-MI area and the MI area in this study was 0.24 for the SC and 0.06 for the SR at the PM level. This result demonstrates that the peak systolic SR of the remote areas at 24 hours of reperfusion do not correlate to the MI size. This result was not surprising since a previous Doppler echocardiography study has already reported that remote areas can show normal contractility (Vartdal et al., 2007).

#### **4.1 Study limitations**

The main limitation of the wavelet de-noising process used here is its sensitivity to artifacts at the B-mode cines. The commercial program compensates for artifacts, such as areas in which the myocardium is shaded by the ribs (black area), by imposing there the averaged values. The wavelet de-noising shows no movement in these areas while the commercial program depicts normal movement. Thus, when applying the wavelet denoising algorithm used here, it is important to include only ultrasound cines with good image quality.

#### **5. Conclusions**

Based on our results we concluded that in the rat model a natural heterogeneity among the strain values exists. Taking into consideration this normal heterogeneity, by measuring the

Strain Measurements Relative to Normal State

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In humans, this kind of study should be performed in the future by normalizing the longitudinal strain relative to baseline and not the circumferential strain as performed here, since the heterogeneity of the strain in humans mostly exists at the longitudinal direction from base to apex (Bachner-Hinenzon et al., 2010).

#### **6. Acknowledgments**

This work was supported by the Chief Scientist, the Ministry of Industry and Commerce Magneton project, the Technion VP for Research and the Alfred Mann Institute at the Technion (AMIT).

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**0**

**3**

**Speckle Reduction in Echocardiography:**

Speckle is the fine-grained texture-like pattern seen in echocardiography, and indeed in all modalities of clinical ultrasound. The application of various image processing techniques to ultrasonography has been explored in the literature, and a common goal is the reduction or removal of the speckle component while preserving image structure. This assumes that speckle is a form of noise which is best removed; a view that is not always shared by those in clinical practice. This chapter presents a thorough overview of current trends in ultrasonic

The phenomenon of speckle formation is described in Section 2 below. A review of the statistical methods used to model speckle is also presented in this chapter. Section 3 then details the main approaches for speckle reduction, covering the most recent of both compounding and post-acquisition techniques. Section 4 of this chapter presents a review and analysis of the methods of evaluation used to rate the performance of various speckle reduction approaches for clinical ultrasound. A particular focus is given to those which include consultation with practising clinicians in the field. The relationship between subjective clinical opinion and some objective image quality metrics on the quality of speckle filter echocardiographic video will be detailed. Details will be presented of a comprehensive evaluation methodology, which aims to combine clinical expertise and numerical assessment.

While the term *ultrasound* can technically be used to refer to all acoustics of frequency greater than the upper threshold of human audibility (*f* > 20 kHz), clinical imaging is generally in the 1-20 MHz range (Rumack et al., 2004). Imaging is based on the transmission of acoustic pulses into the body, which interact with the tissue medium. Echoes are reflected by interfaces between tissue of differing acoustic properties, which are detected by a receiver. If the propagation velocity of sound waves in the imaged medium is known, the depth of interactions giving rise to the echoes can be determined. Characteristics of the returned signal (e.g. amplitude, phase) provide information on the interaction, and indicate the nature of the media involved. The amplitude of the reflected signal is used to produce ultrasound images, while the frequency shifts provide information on moving targets such as blood. Fig.

speckle reduction techniques, with an emphasis on echocardiography.

1 displays examples of clinical echocardiograms containing speckle.

Finally, Section 5 will conclude the chapter.

**2. Speckle formation and statistics**

**1. Introduction**

**Trends and Perceptions**

*National University of Ireland, Galway*

*Republic of Ireland*

Seán Finn, Martin Glavin and Edward Jones


### **Speckle Reduction in Echocardiography: Trends and Perceptions**

Seán Finn, Martin Glavin and Edward Jones *National University of Ireland, Galway Republic of Ireland*

#### **1. Introduction**

40 Echocardiography – New Techniques

Schiller NB, Shah PM, Crawford M, DeMaria A, Devereux R, Feigenbaum H, Gutgesell H,

2007.

Reichek N, Sahn D, Schnittger I, et al. Recommendations for quantitation of the left ventricle by two-dimensional echocardiography. American Society of Echocardiography Committee on Standards, Subcommittee on Quantitation of Two-Dimensional Echocardiograms. J Am Soc Echocardiogr. 2(5):358-67, 1989. Vartdal T, Brunvand H, Pettersen E, Smith HJ, Lyseggen E, Helle-Valle T, Skulstad H, Ihlen

H, Edvardsen T. Early prediction of infarct size by strain Doppler echocardiography after coronary reperfusion. J Am Coll Cardiol. 24;49(16):1715-,

> Speckle is the fine-grained texture-like pattern seen in echocardiography, and indeed in all modalities of clinical ultrasound. The application of various image processing techniques to ultrasonography has been explored in the literature, and a common goal is the reduction or removal of the speckle component while preserving image structure. This assumes that speckle is a form of noise which is best removed; a view that is not always shared by those in clinical practice. This chapter presents a thorough overview of current trends in ultrasonic speckle reduction techniques, with an emphasis on echocardiography.

> The phenomenon of speckle formation is described in Section 2 below. A review of the statistical methods used to model speckle is also presented in this chapter. Section 3 then details the main approaches for speckle reduction, covering the most recent of both compounding and post-acquisition techniques. Section 4 of this chapter presents a review and analysis of the methods of evaluation used to rate the performance of various speckle reduction approaches for clinical ultrasound. A particular focus is given to those which include consultation with practising clinicians in the field. The relationship between subjective clinical opinion and some objective image quality metrics on the quality of speckle filter echocardiographic video will be detailed. Details will be presented of a comprehensive evaluation methodology, which aims to combine clinical expertise and numerical assessment. Finally, Section 5 will conclude the chapter.

#### **2. Speckle formation and statistics**

While the term *ultrasound* can technically be used to refer to all acoustics of frequency greater than the upper threshold of human audibility (*f* > 20 kHz), clinical imaging is generally in the 1-20 MHz range (Rumack et al., 2004). Imaging is based on the transmission of acoustic pulses into the body, which interact with the tissue medium. Echoes are reflected by interfaces between tissue of differing acoustic properties, which are detected by a receiver. If the propagation velocity of sound waves in the imaged medium is known, the depth of interactions giving rise to the echoes can be determined. Characteristics of the returned signal (e.g. amplitude, phase) provide information on the interaction, and indicate the nature of the media involved. The amplitude of the reflected signal is used to produce ultrasound images, while the frequency shifts provide information on moving targets such as blood. Fig. 1 displays examples of clinical echocardiograms containing speckle.

Trends and Perceptions 3

Speckle Reduction in Echocardiography: Trends and Perceptions 43

Depending on the nature of the interface, two types of reflection are observed: *Specular Reflection* occurs when the interface is large and smooth with respect to the ultrasound pulse wavelength, e.g. the diaphragm and a urine filled bladder (Rumack et al., 2004). Strong clear reflections are produced, in the same fashion as for a mirror. Detection of these echoes is highly dependent on the angle of insonification (Rumack et al., 2004). *Scattering* results from interfaces much smaller than the wavelength of the ultrasound pulse. A volume of small scattering interfaces such as blood cells or a non smooth organ surface produce echoes which are scattered in all directions. This collection of scatterers are said to act as a diffuse reflector. The constructive and destructive interference of these scattered echoes results in a granular

> sin *θ*<sup>1</sup> sin *θ*<sup>2</sup>

where the quantities *θ*1, *θ*2, *c*1, and *c*<sup>2</sup> are respectively the angles of incidence and refraction, and the corresponding speeds of propagation. Attenuation of the acoustic pulse is mainly due to absorption and scattering (Quistgaard, 1997), and can be modelled as: *A*(*x*, *t*) = *A*(*x*, 0)*e*−*<sup>α</sup> <sup>f</sup>* <sup>2</sup>*<sup>x</sup>* (Thijssen, 2003). where *A*(*x*, *t*) is the amplitude at depth *x* and time *t*, *f* is the frequency and *α* is the attenuation coefficient. Generally attenuation is quite severe: in (Quistgaard, 1997), a halving of intensity every 0.8 cm at 5 MHz operation is described.

The interference experienced by reflections from diffuse scatterers result in a granular pattern known as speckle. Speckle is common to all imaging systems using coherent waves for illumination, including laser and radar imagery. In echocardiography, speckle noise is prominent in all cross-sectional views (Massay et al., 1989), and its effect is far more significant

The basic description of ultrasound speckle in the literature is based on the characterisation of laser speckle by Goodman (Goodman, 1975; 1976). This approach is extended to acoustic imagery by a number of authors (Burckhardt, 1978; Wagner et al., 1988; 1983). Burckhardt (Burckhardt, 1978) notes that despite its random appearance, speckle is essentially deterministic: scans under identical situations produce the same speckle pattern. This behaviour is in contrast to that of true stochastic processes such as electrical noise. There is no direct relationship between the imaged medium and the observed speckle pattern however. If the same object is imaged with different imaging parameters, the speckle pattern produced is quite different. Burckhardt thus concludes that the speckle pattern has only a tenuous relationship to the imaged medium, and is instead dependant on the parameters of the imaging system. The size of the speckle granules are of similar size to the resolution of the scanner, in both axial and lateral directions. Burckhardt justifies the treatment of pulsed acoustics as a coherent wave source in the situation where the each pulse contains a number

Each ultrasound pulse encloses a three dimensional volume which defines the smallest resolvable structure, which is known as the resolution cell. The nature of the speckle at an image location is determined by the number of diffuse scatterers which are present in the resolution cell at the relevant position in the imaged medium. If the number of scatterers is large and randomly positioned, the resulting pattern is known as fully formed (or fully developed) speckle. In this case the speckle pattern depends only on the imaging system.

<sup>=</sup> *<sup>c</sup>*<sup>1</sup> *c*2

(2)

artefact known as *speckle*. Refraction is governed by Snell's law:

than additive noise sources such as sensor noise (Zong et al., 1998).

of cycles of the carrier wave.

The propagation speed in tissue varies with tissue type, temperature and pressure. Assuming constant temperature and pressure in the body, only the tissue type is considered (Quistgaard, 1997). The mean speed of sound propagation in human soft tissue is generally taken as 1540 m/s. Acoustic pulses transmitted into the body can experience:


The acoustic impedance of a medium (*Z*) is the product of its density, *ρ*, and the speed of acoustic propagation in that medium, *c* (*Z* = *ρc*).

The strength of reflection at an interface depends on the difference in acoustic impedance on each side of the boundary, as well as the size of the interface, its surface characteristics, and the angle of insonification. (Middleton & Kurtz, 2004; Rumack et al., 2004). The reflection coefficient at the interface is given in the same manner as the analogous case of electromagnetic propagation:

$$\Gamma = \frac{\mathbf{Z}\_2 - \mathbf{Z}\_1}{\mathbf{Z}\_2 + \mathbf{Z}\_1} \tag{1}$$

(a) (b)

Fig. 1. Clinical ultrasound images, used in speckle filter evaluation.

2 Will-be-set-by-IN-TECH

The propagation speed in tissue varies with tissue type, temperature and pressure. Assuming constant temperature and pressure in the body, only the tissue type is considered (Quistgaard, 1997). The mean speed of sound propagation in human soft tissue is generally taken as 1540

**Reflection:** Also known a backscatter, reflection occurs when an acoustic pulse encounters an

**Refraction:** When sound waves pass through an interface between media of different

**Absorption:** Energy from the acoustic pulse is absorbed into the tissue, by conversion to

The acoustic impedance of a medium (*Z*) is the product of its density, *ρ*, and the speed of

The strength of reflection at an interface depends on the difference in acoustic impedance on each side of the boundary, as well as the size of the interface, its surface characteristics, and the angle of insonification. (Middleton & Kurtz, 2004; Rumack et al., 2004). The reflection coefficient at the interface is given in the same manner as the analogous case of

> <sup>Γ</sup> <sup>=</sup> *<sup>Z</sup>*<sup>2</sup> <sup>−</sup> *<sup>Z</sup>*<sup>1</sup> *Z*<sup>2</sup> + *Z*<sup>1</sup>

(a) (b)

(c) (d)

Fig. 1. Clinical ultrasound images, used in speckle filter evaluation.

(1)

m/s. Acoustic pulses transmitted into the body can experience:

interface between tissues of differing acoustic impedances.

acoustic propagation in that medium, *c* (*Z* = *ρc*).

thermal energy.

electromagnetic propagation:

propagation speeds, a change in the direction of propagation occurs.

Depending on the nature of the interface, two types of reflection are observed: *Specular Reflection* occurs when the interface is large and smooth with respect to the ultrasound pulse wavelength, e.g. the diaphragm and a urine filled bladder (Rumack et al., 2004). Strong clear reflections are produced, in the same fashion as for a mirror. Detection of these echoes is highly dependent on the angle of insonification (Rumack et al., 2004). *Scattering* results from interfaces much smaller than the wavelength of the ultrasound pulse. A volume of small scattering interfaces such as blood cells or a non smooth organ surface produce echoes which are scattered in all directions. This collection of scatterers are said to act as a diffuse reflector. The constructive and destructive interference of these scattered echoes results in a granular artefact known as *speckle*. Refraction is governed by Snell's law:

$$\frac{\sin \theta\_1}{\sin \theta\_2} = \frac{c\_1}{c\_2} \tag{2}$$

where the quantities *θ*1, *θ*2, *c*1, and *c*<sup>2</sup> are respectively the angles of incidence and refraction, and the corresponding speeds of propagation. Attenuation of the acoustic pulse is mainly due to absorption and scattering (Quistgaard, 1997), and can be modelled as: *A*(*x*, *t*) = *A*(*x*, 0)*e*−*<sup>α</sup> <sup>f</sup>* <sup>2</sup>*<sup>x</sup>* (Thijssen, 2003). where *A*(*x*, *t*) is the amplitude at depth *x* and time *t*, *f* is the frequency and *α* is the attenuation coefficient. Generally attenuation is quite severe: in (Quistgaard, 1997), a halving of intensity every 0.8 cm at 5 MHz operation is described.

The interference experienced by reflections from diffuse scatterers result in a granular pattern known as speckle. Speckle is common to all imaging systems using coherent waves for illumination, including laser and radar imagery. In echocardiography, speckle noise is prominent in all cross-sectional views (Massay et al., 1989), and its effect is far more significant than additive noise sources such as sensor noise (Zong et al., 1998).

The basic description of ultrasound speckle in the literature is based on the characterisation of laser speckle by Goodman (Goodman, 1975; 1976). This approach is extended to acoustic imagery by a number of authors (Burckhardt, 1978; Wagner et al., 1988; 1983). Burckhardt (Burckhardt, 1978) notes that despite its random appearance, speckle is essentially deterministic: scans under identical situations produce the same speckle pattern. This behaviour is in contrast to that of true stochastic processes such as electrical noise. There is no direct relationship between the imaged medium and the observed speckle pattern however. If the same object is imaged with different imaging parameters, the speckle pattern produced is quite different. Burckhardt thus concludes that the speckle pattern has only a tenuous relationship to the imaged medium, and is instead dependant on the parameters of the imaging system. The size of the speckle granules are of similar size to the resolution of the scanner, in both axial and lateral directions. Burckhardt justifies the treatment of pulsed acoustics as a coherent wave source in the situation where the each pulse contains a number of cycles of the carrier wave.

Each ultrasound pulse encloses a three dimensional volume which defines the smallest resolvable structure, which is known as the resolution cell. The nature of the speckle at an image location is determined by the number of diffuse scatterers which are present in the resolution cell at the relevant position in the imaged medium. If the number of scatterers is large and randomly positioned, the resulting pattern is known as fully formed (or fully developed) speckle. In this case the speckle pattern depends only on the imaging system.

Trends and Perceptions 5

Speckle Reduction in Echocardiography: Trends and Perceptions 45

• Speckle introduces spurious 'false-fine' structures, which give the appearance of resolution

• Small grey level differences can be masked (Burckhardt, 1978), which can obscure tissue

• Human interpretation of ultrasonography can be negatively impacted (Abd-Elmoniem et al., 2002; Zhang et al., 2007; Zong et al., 1998), introducing a degree of subjectivity (Dantas & Costa, 2007). The presence of speckle has been determined to be the cause of an eight-fold reduction in lesion detectability (Bamber & Daft, 1986). Reduction of echocardiographic speckle has been shown to positively affect subjective image quality

• The effectiveness (speed and accuracy) of automated processing tasks is also reduced by speckle (Abd-Elmoniem et al., 2002; Yu & Acton, 2002; Zhang et al., 2007; Zong et al.,

• While speckle can be viewed as deterministic (Dantas et al., 2005), it does not contain

Approaches to speckle reduction can be broadly grouped into compounding and

These techniques combine two or more images of the same area. The measurements from image structure will be partially correlated, while the speckle pattern will differ. Compounding these images (e.g. by averaging) results in an image with enhanced structure and a reduced speckle pattern. A number of different scanning methods can be used to produce the images to be compounded. Frequency compounding uses images with separate frequency ranges within the transducer bandwidth (Galloway et al., 1988; Gehlbach & Sommer, 1987; Magnin et al., 1982; Trahey, Allison, Smith & von Ramm, 1986). A common technique is spilt spectrum processing (SSP) (Bamber & Phelps, 1991; Newhouse et al., 1982; Stetson et al., 1997), in which the wideband RF signal is split into a number of subbands using bandpass filters. Envelope detection of these RF subbands yields amplitude data, which is combined to produce an image with enhanced structure and reduced speckle component. The recent method of Dantas and Costa (Dantas & Costa, 2007) is applied to the entire 2D RF image. This is in contrast to some SSP methods, which are applied to each 1D RF scan line individually. The RF image was decomposed into a number of orientation specific subbands by use of a bank of modified log Gabor filters. Each subband RF image was used to generate an amplitude image, and the final speckle reduced image was produced by compounding these amplitude images. The technique was tested by application to simulated images and comparison to maximally speckle free reference images generated

Other compounding approaches include spatial compounding, which combine multiple images from different scan directions (O'Donnell & Silverstein, 1988; Pai-Chi & O'Donnell, 1994; Trahey, Smith & von Ramm, 1986). Burckhardt (Burckhardt, 1978) showed that in order for these scans to be independent of each other (and so having uncorrelated speckle patterns), the transducer must be translated by approximately half its element width.

beyond that of the imaging system (Dantas et al., 2005).

boundaries (Dantas & Costa, 2007; Dantas et al., 2005).

and improve boundary definition (Massay et al., 1989).

postacquisition methods.

**3.1 Compounding approaches**

using the method of Burckhardt (Burckhardt, 1978).

1998), such as edge detection, segmentation and registration.

information on the imaged structure in the fully developed speckle case.

• Image contrast is reduced (Dantas & Costa, 2007; Zhang et al., 2007).

Wagner *et al.* (Wagner et al., 1983) show that in the case of a mixture of diffuse and specular scattering, the speckle pattern is related to the underlying texture of the medium.

The randomly scattered echoes from the scatterers are summed within each resolution cell. These echoes are sinusoidal in nature. Expressed as phasors, the summation is described as a random walk of the real and imaginary components. In the case of fully developed speckle, and with uniformly distributed phase values between 0 and 2*π*, these components have a circular Gaussian distribution (Wagner et al., 1983):

$$p(a\_r, a\_i) = \frac{1}{2\pi\sigma^2} \exp\left(-\frac{a\_r^2 + a\_i^2}{2\sigma^2}\right) \tag{3}$$

where (*ar*, *ai*) are the real and imaginary components. The amplitude within each resolution cell, *A* = *a*2 *<sup>r</sup>* + *a*<sup>2</sup> *<sup>i</sup>* , is then given by a Rayleigh distribution:

$$p(A) = \frac{A}{\Psi} \exp\left(-\frac{A^2}{2\psi}\right), \quad A \ge 0 \tag{4}$$

The Rayleigh parameter *ψ* depends on the mean square scattering amplitude of the medium (Goodman, 1975). Burckhardt defined an SNR measure for the amplitude as *SNRA* = *A*¯/*σA*. i.e. the ratio of mean to standard deviation. It can be shown that *SNRA* = 1.91 for the Rayleigh distribution of fully developed speckle. Burckhardt explores the statistics of image compounded from multiple individual scans, and demonstrates a method of simulating a theoretically maximally speckle free image from a known structure. Alternative distributions to Rayleigh have been proposed for situations not meeting the requirements of fully developed speckle, such as insufficient numbers of scatterers per resolution cell, or non random positioning. These include the Rician, Nakagami and *K* distributions (Shankar et al., 2001; Shankar, 1995; Smolíovái et al., 2004).

The number of scatterers required for fully formed speckle varies in the literature. Ten or greater is a common figure (Krissian et al., 2007; Lizzi et al., 1997; Thijssen, 2003), although it is stated in (Ng et al., 2006) that at least thirty scatterers should be present for the central limit theorem to hold. It has also been shown that neither the number of scatterers or their random positioning are required for fully developed speckle governed by Rayleigh statistics (Dantas et al., 2005): a sparse set of uniformly positioned equivalent scatters can also produce a fully formed speckle pattern.

#### **3. Techniques for reducing speckle**

The reduction of speckle while preserving image structure is a challenging image processing problem, due to the multiplicative-like behaviour of speckle. This can is evident from the relatively large volume of literature dedicated methods of reducing or eliminating speckle. The common justifications for the removal of speckle in these works are the general reduction in image quality due to the presence of speckle. However, the question of whether or not to remove speckle as noise in clinical imagery is an open one, and depends largely on the application. A number of specific negative effects of speckle, and benefits of its removal in clinical ultrasonography have been noted:


Approaches to speckle reduction can be broadly grouped into compounding and postacquisition methods.

#### **3.1 Compounding approaches**

4 Will-be-set-by-IN-TECH

Wagner *et al.* (Wagner et al., 1983) show that in the case of a mixture of diffuse and specular

The randomly scattered echoes from the scatterers are summed within each resolution cell. These echoes are sinusoidal in nature. Expressed as phasors, the summation is described as a random walk of the real and imaginary components. In the case of fully developed speckle, and with uniformly distributed phase values between 0 and 2*π*, these components have a

<sup>2</sup>*πσ*<sup>2</sup> exp

where (*ar*, *ai*) are the real and imaginary components. The amplitude within each resolution

 − *A*2 2*ψ* 

The Rayleigh parameter *ψ* depends on the mean square scattering amplitude of the medium (Goodman, 1975). Burckhardt defined an SNR measure for the amplitude as *SNRA* = *A*¯/*σA*. i.e. the ratio of mean to standard deviation. It can be shown that *SNRA* = 1.91 for the Rayleigh distribution of fully developed speckle. Burckhardt explores the statistics of image compounded from multiple individual scans, and demonstrates a method of simulating a theoretically maximally speckle free image from a known structure. Alternative distributions to Rayleigh have been proposed for situations not meeting the requirements of fully developed speckle, such as insufficient numbers of scatterers per resolution cell, or non random positioning. These include the Rician, Nakagami and *K* distributions (Shankar et al.,

The number of scatterers required for fully formed speckle varies in the literature. Ten or greater is a common figure (Krissian et al., 2007; Lizzi et al., 1997; Thijssen, 2003), although it is stated in (Ng et al., 2006) that at least thirty scatterers should be present for the central limit theorem to hold. It has also been shown that neither the number of scatterers or their random positioning are required for fully developed speckle governed by Rayleigh statistics (Dantas et al., 2005): a sparse set of uniformly positioned equivalent scatters can also produce

The reduction of speckle while preserving image structure is a challenging image processing problem, due to the multiplicative-like behaviour of speckle. This can is evident from the relatively large volume of literature dedicated methods of reducing or eliminating speckle. The common justifications for the removal of speckle in these works are the general reduction in image quality due to the presence of speckle. However, the question of whether or not to remove speckle as noise in clinical imagery is an open one, and depends largely on the application. A number of specific negative effects of speckle, and benefits of its removal in

 − *a*2 *<sup>r</sup>* + *a*<sup>2</sup> *i* 2*σ*<sup>2</sup>

, *A* ≥ 0 (4)

(3)

scattering, the speckle pattern is related to the underlying texture of the medium.

*<sup>p</sup>*(*ar*, *ai*) = <sup>1</sup>

*<sup>i</sup>* , is then given by a Rayleigh distribution:

*<sup>ψ</sup>* exp

*<sup>p</sup>*(*A*) = *<sup>A</sup>*

circular Gaussian distribution (Wagner et al., 1983):

2001; Shankar, 1995; Smolíovái et al., 2004).

a fully formed speckle pattern.

**3. Techniques for reducing speckle**

clinical ultrasonography have been noted:

cell, *A* =

 *a*2 *<sup>r</sup>* + *a*<sup>2</sup>

> These techniques combine two or more images of the same area. The measurements from image structure will be partially correlated, while the speckle pattern will differ. Compounding these images (e.g. by averaging) results in an image with enhanced structure and a reduced speckle pattern. A number of different scanning methods can be used to produce the images to be compounded. Frequency compounding uses images with separate frequency ranges within the transducer bandwidth (Galloway et al., 1988; Gehlbach & Sommer, 1987; Magnin et al., 1982; Trahey, Allison, Smith & von Ramm, 1986). A common technique is spilt spectrum processing (SSP) (Bamber & Phelps, 1991; Newhouse et al., 1982; Stetson et al., 1997), in which the wideband RF signal is split into a number of subbands using bandpass filters. Envelope detection of these RF subbands yields amplitude data, which is combined to produce an image with enhanced structure and reduced speckle component. The recent method of Dantas and Costa (Dantas & Costa, 2007) is applied to the entire 2D RF image. This is in contrast to some SSP methods, which are applied to each 1D RF scan line individually. The RF image was decomposed into a number of orientation specific subbands by use of a bank of modified log Gabor filters. Each subband RF image was used to generate an amplitude image, and the final speckle reduced image was produced by compounding these amplitude images. The technique was tested by application to simulated images and comparison to maximally speckle free reference images generated using the method of Burckhardt (Burckhardt, 1978).

> Other compounding approaches include spatial compounding, which combine multiple images from different scan directions (O'Donnell & Silverstein, 1988; Pai-Chi & O'Donnell, 1994; Trahey, Smith & von Ramm, 1986). Burckhardt (Burckhardt, 1978) showed that in order for these scans to be independent of each other (and so having uncorrelated speckle patterns), the transducer must be translated by approximately half its element width.

Trends and Perceptions 7

Speckle Reduction in Echocardiography: Trends and Perceptions 47

Massay *et al.* (Massay et al., 1989) proposed a method of speckle reduction using local

Perona and Malik (Perona & Malik, 1990) introduced the first anisotropic diffusion method for additive noise. This is an iterative method of smoothing an image, similar in concept to

A diffusion function is calculated at each iteration, with the aim of inhibiting smoothing across image edges and permitting it in homogeneous areas. Diffusion takes place according to the

where *I*(*x*, *y*; *t*) is the image under diffusion, *t* is an artificial time dimension representing the progress of diffusion, *I*<sup>0</sup> is the observed image, ∇ and ∇ · () are the gradient and divergence operators, and |·| represents magnitude. The diffusion function *c*(·) controls the level of diffusion at each image position. Smoothing is inhibited across image edges by choosing a monotonically decreasing function of gradient magnitude for *c*(|∇*I*(*x*, *y*; *t*)|),

histogram integral. A number of extensions to this method have been proposed, most notably that of Catté *et al.* (Catté et al., 1992), who regularised the calculation of *c*(·). This makes (5) mathematically well-posed, having a unique solution. While this method is capable of intra-region smoothing with edge preservation for images corrupted with additive noise, its effect on images corrupted with multiplicative noise is less than satisfactory (Yu & Acton,

To address the unsiutablility of Perona and Malik's diffusion for multiplicative speckled situations, Yu and Acton (Yu & Acton, 2002) proposed a diffusion function based on the

In contrast to (5), the diffusion function *c*(.) is not a function of the gradient magnitude, but rather of the Instantaneous Coefficient of Variation (ICOV) *q*. The ICOV is based on the variation coefficient used in SAR filtering as a signal/edge discriminator, and is defined as:

[1 + (0.25)

<sup>1</sup> <sup>+</sup> *<sup>q</sup>*2(*x*, *<sup>y</sup>*, *<sup>t</sup>*) <sup>−</sup> *<sup>q</sup>*<sup>2</sup>

*q*2(*x*, *y*, *t*)(1 + *q*<sup>2</sup>

*<sup>∂</sup><sup>t</sup>* <sup>=</sup> ∇·{*c*(|∇*Iσ*(*x*, *<sup>y</sup>*; *<sup>t</sup>*)|).∇*I*(*x*, *<sup>y</sup>*; *<sup>t</sup>*)}, *<sup>I</sup>*(*x*, *<sup>y</sup>*; 0) = *<sup>I</sup>*0(*x*, *<sup>y</sup>*) (5)

. Here *k* is an edge threshold, set to 90% of the absolute gradient

*<sup>∂</sup><sup>t</sup>* <sup>=</sup> <sup>∇</sup>.[*c*(*q*).∇*I*(*x*, *<sup>y</sup>*, *<sup>t</sup>*)], *<sup>I</sup>*(*x*, *<sup>y</sup>*, 0) = *<sup>I</sup>*0(*x*, *<sup>y</sup>*) (6)

<sup>−</sup> (0.25)<sup>2</sup>

 <sup>∇</sup><sup>2</sup> *<sup>I</sup> I*   <sup>∇</sup><sup>2</sup> *<sup>I</sup> I* 2

<sup>0</sup>(*t*)

0(*t*))−<sup>1</sup>

]<sup>2</sup> (7)

(8)

statistics: the level of smoothing is determined by an estimate of local speckle level.

**3.2.2 Diffusion filtering**

following Partial Differential Equation (PDE):

coefficient of variation used in synthetic aperture radar:

*q*(*x*, *y*, *t*) =

*c* [*q*(*x*, *y*, *t*), *q*0(*t*)] =

 (0.5) | ∇*I I* | 2

where <sup>∇</sup><sup>2</sup> is the Laplacian operator. The diffusion function *<sup>c</sup>*(.) used here is:

*∂I*(*x*, *y*, *t*)

*∂I*(*x*, *y*; *t*)

such as *c*(*x*) = *e*−(*x*/*k*)<sup>2</sup>

2002).

heat diffusion.

Temporal compounding (frame averaging) operates as the name suggests by combining scans performed over time. This approach suffers from a dependence on motion: in a still medium the speckle pattern will not change. Conversely, fast moving organs such as the heart may appear smeared with this method. Some modern ultrasound system are capable of performing spatial compounding by sweeping the scan beam over the medium, while the transducer is held statically (Jespersen et al., 2000). A recent transducer design makes use of a particular arrangement of receive elements to acquire multiple independent images simultaneously (Behar et al., 2003).

#### **3.2 Postacquisition speckle reduction**

Postacquisition methods operate on the image after it has been envelope detected, and have the advantage of not requiring a specific mode of scanning, or access to the RF data. Aa simulation study comparing postacquisition filters to spatial compounding reported better image improvement for filtering, in terms of speckle reduction and image quality (Adam et al., 2006). The number of postacquisition speckle reduction methods in the literature is large, and the selection detailed here are grouped according to their general approach.

#### **3.2.1 Adaptive filters**

Adaptive filters attempt to adjust the level of filtering at each image location. The Lee filter (Lee, 1980; 1981), Kuan filter (Kuan et al., 1987) and Frost filter (Frost et al., 1982) were proposed for the task of speckle removal in synthetic aperture radar (SAR), and assume a multiplicative model for speckle noise. Enhanced versions of the Lee and Frost filter were also proposed (Lopes et al., 1990). These are improved by the classification of image pixels into a number of classes, and filtering accordingly. The method of Bamber and Daft (Bamber & Daft, 1986) extended this adaptive approach to ultrasound images by varying the degree of smoothing according to a local estimate of the level of speckle.

Median filtering was extended to the case of speckle removal by Loupas *et al.* (Loupas et al., 1989). This approach replaced pixels with the weighted median of a dynamically sized window, and is known as the adaptive weighted median filter (AWMF). Region growing techniques such as (Chen et al., 2003; Huang et al., 2003; Karaman et al., 1995; Koo & Park, 1991) have been applied to ultrasonography. Pixels are grouped in these methods, according to similarity of intensity and connectivity. Spatial filtering is performed to extend these regions, and the challenge is the selection of appropriate similarity criteria.

A recently proposed method by Tay *et al.* (Tay et al., 2006a;b) used an iterative technique of speckle reduction by the removal of outliers. The locale around each pixel is examined, and local extrema are replaced with a local average. This process is repeated until no further outliers are found. Thus the filter reduces the local variance around each pixel, and is referred to by the authors as the "Squeeze Box" filter.

The non-local means filter of Coupé *et al.* (Coupé et al., 2009) estimates the true value of each pixel as the weighted sum of the windowed averages of within a search volume centred at the pixel of interest. This technique was adapted to speckled ultrasonography by incorporation of a multiplicative noise model by Bayesian estimation.

Massay *et al.* (Massay et al., 1989) proposed a method of speckle reduction using local statistics: the level of smoothing is determined by an estimate of local speckle level.

#### **3.2.2 Diffusion filtering**

6 Will-be-set-by-IN-TECH

Temporal compounding (frame averaging) operates as the name suggests by combining scans performed over time. This approach suffers from a dependence on motion: in a still medium the speckle pattern will not change. Conversely, fast moving organs such as the heart may appear smeared with this method. Some modern ultrasound system are capable of performing spatial compounding by sweeping the scan beam over the medium, while the transducer is held statically (Jespersen et al., 2000). A recent transducer design makes use of a particular arrangement of receive elements to acquire multiple independent images

Postacquisition methods operate on the image after it has been envelope detected, and have the advantage of not requiring a specific mode of scanning, or access to the RF data. Aa simulation study comparing postacquisition filters to spatial compounding reported better image improvement for filtering, in terms of speckle reduction and image quality (Adam et al., 2006). The number of postacquisition speckle reduction methods in the literature is large, and

Adaptive filters attempt to adjust the level of filtering at each image location. The Lee filter (Lee, 1980; 1981), Kuan filter (Kuan et al., 1987) and Frost filter (Frost et al., 1982) were proposed for the task of speckle removal in synthetic aperture radar (SAR), and assume a multiplicative model for speckle noise. Enhanced versions of the Lee and Frost filter were also proposed (Lopes et al., 1990). These are improved by the classification of image pixels into a number of classes, and filtering accordingly. The method of Bamber and Daft (Bamber & Daft, 1986) extended this adaptive approach to ultrasound images by varying the

Median filtering was extended to the case of speckle removal by Loupas *et al.* (Loupas et al., 1989). This approach replaced pixels with the weighted median of a dynamically sized window, and is known as the adaptive weighted median filter (AWMF). Region growing techniques such as (Chen et al., 2003; Huang et al., 2003; Karaman et al., 1995; Koo & Park, 1991) have been applied to ultrasonography. Pixels are grouped in these methods, according to similarity of intensity and connectivity. Spatial filtering is performed to extend these

A recently proposed method by Tay *et al.* (Tay et al., 2006a;b) used an iterative technique of speckle reduction by the removal of outliers. The locale around each pixel is examined, and local extrema are replaced with a local average. This process is repeated until no further outliers are found. Thus the filter reduces the local variance around each pixel, and is referred

The non-local means filter of Coupé *et al.* (Coupé et al., 2009) estimates the true value of each pixel as the weighted sum of the windowed averages of within a search volume centred at the pixel of interest. This technique was adapted to speckled ultrasonography by incorporation

the selection detailed here are grouped according to their general approach.

degree of smoothing according to a local estimate of the level of speckle.

regions, and the challenge is the selection of appropriate similarity criteria.

to by the authors as the "Squeeze Box" filter.

of a multiplicative noise model by Bayesian estimation.

simultaneously (Behar et al., 2003).

**3.2.1 Adaptive filters**

**3.2 Postacquisition speckle reduction**

Perona and Malik (Perona & Malik, 1990) introduced the first anisotropic diffusion method for additive noise. This is an iterative method of smoothing an image, similar in concept to heat diffusion.

A diffusion function is calculated at each iteration, with the aim of inhibiting smoothing across image edges and permitting it in homogeneous areas. Diffusion takes place according to the following Partial Differential Equation (PDE):

$$\frac{\partial I(\mathbf{x}, y; t)}{\partial t} = \nabla \cdot \{c(|\nabla I\_{\mathcal{T}}(\mathbf{x}, y; t)|) \cdot \nabla I(\mathbf{x}, y; t)\}, \quad I(\mathbf{x}, y; 0) = I\_0(\mathbf{x}, y) \tag{5}$$

where *I*(*x*, *y*; *t*) is the image under diffusion, *t* is an artificial time dimension representing the progress of diffusion, *I*<sup>0</sup> is the observed image, ∇ and ∇ · () are the gradient and divergence operators, and |·| represents magnitude. The diffusion function *c*(·) controls the level of diffusion at each image position. Smoothing is inhibited across image edges by choosing a monotonically decreasing function of gradient magnitude for *c*(|∇*I*(*x*, *y*; *t*)|), such as *c*(*x*) = *e*−(*x*/*k*)<sup>2</sup> . Here *k* is an edge threshold, set to 90% of the absolute gradient histogram integral. A number of extensions to this method have been proposed, most notably that of Catté *et al.* (Catté et al., 1992), who regularised the calculation of *c*(·). This makes (5) mathematically well-posed, having a unique solution. While this method is capable of intra-region smoothing with edge preservation for images corrupted with additive noise, its effect on images corrupted with multiplicative noise is less than satisfactory (Yu & Acton, 2002).

To address the unsiutablility of Perona and Malik's diffusion for multiplicative speckled situations, Yu and Acton (Yu & Acton, 2002) proposed a diffusion function based on the coefficient of variation used in synthetic aperture radar:

$$\frac{\partial I(\mathbf{x}, y, t)}{\partial t} = \nabla.[c(q).\nabla I(\mathbf{x}, y, t)], \quad I(\mathbf{x}, y, 0) = I\_0(\mathbf{x}, y) \tag{6}$$

In contrast to (5), the diffusion function *c*(.) is not a function of the gradient magnitude, but rather of the Instantaneous Coefficient of Variation (ICOV) *q*. The ICOV is based on the variation coefficient used in SAR filtering as a signal/edge discriminator, and is defined as:

$$q(\mathbf{x}, y, t) = \sqrt{\frac{(0.5) \left( |\frac{\nabla I}{I}| \right)^2 - (0.25)^2 \left( \frac{\nabla^2 I}{I} \right)^2}{[1 + (0.25) \left( \frac{\nabla^2 I}{I} \right)]^2}} \tag{7}$$

where <sup>∇</sup><sup>2</sup> is the Laplacian operator. The diffusion function *<sup>c</sup>*(.) used here is:

$$c\left[q(\mathbf{x},\mathbf{y},t),q\_0(t)\right] = \left(1 + \frac{q^2(\mathbf{x},\mathbf{y},t) - q\_0^2(t)}{q^2(\mathbf{x},\mathbf{y},t)(1 + q\_0^2(t))}\right)^{-1} \tag{8}$$

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Speckle Reduction in Echocardiography: Trends and Perceptions 49

The eigenvectors of *T<sup>ρ</sup>* are denoted by (*ω*� 1, *ω*� <sup>2</sup>), and the corresponding eigenvalues by (*μ*1, *μ*2). If the eigenvalues are ordered so that *μ*<sup>1</sup> ≥ *μ*2, then (*ω*� 1, *ω*� <sup>2</sup>) give the directions of maximum and minimum local variation, respectively. These are the directions normal and tangent to the local image gradient, the gradient and contour directions. The corresponding eigenvalues give the strength of the gradient in these directions, and also provide information on the local coherence or anisotropy. A measure of local coherence is defined as *<sup>κ</sup>* = (*μ*<sup>1</sup> <sup>−</sup> *<sup>μ</sup>*2)<sup>2</sup>

where *D* is the diffusion matrix, constructed with the same eigenvectors as *T<sup>ρ</sup>* (�*e*<sup>1</sup> = *ω*� 1,�*e*<sup>2</sup> =

The nonlinear coherent diffusion (NCD) method of Abd-Elmoniem *et al.* (Abd-Elmoniem et al., 2002) is a tensor valued anisotropic diffusion scheme for the removal of speckle. The eigenvalues of the diffusion tensor define the directional strength of diffusion at each image location, and these are chosen to reflect an estimate of the strength of speckle at that location. Image regions closely resembling fully developed speckle are mean filtered, while those dissimilar remain unaltered. Similar to the CED method, this approach uses a tensor-valued diffusion function, calculated as a component-wise convolution of a

*<sup>c</sup>*<sup>1</sup> + (<sup>1</sup> <sup>−</sup> *<sup>c</sup>*1) exp <sup>−</sup>*c*<sup>2</sup>

*<sup>δ</sup><sup>t</sup>* <sup>=</sup> <sup>∇</sup>.(*D*∇*I*(*x*, *<sup>y</sup>*, *<sup>t</sup>*)) (13)

, otherwise (14)

(15)

*c*1, if *μ*<sup>1</sup> = *μ*<sup>2</sup>

*κ* 

*<sup>x</sup> K<sup>ρ</sup>* ∗ *Ixy <sup>K</sup><sup>ρ</sup>* <sup>∗</sup> *Ixy <sup>K</sup><sup>ρ</sup>* <sup>∗</sup> *<sup>I</sup>*<sup>2</sup>

0, otherwise , *<sup>λ</sup>*<sup>2</sup> <sup>=</sup> *<sup>α</sup>* (16)

*y* 

(Weickert, 1999). The CED diffusion process is described by the PDE:

where *c*<sup>1</sup> and *c*<sup>2</sup> are parameters constrained by 0 < *c*<sup>1</sup> � 1 and *c*<sup>2</sup> > 0.

same eigenvectors as *Jρ*, but with eigenvalues *λ*1, *λ*<sup>2</sup> defined as:

 *α* <sup>1</sup> <sup>−</sup> *<sup>κ</sup> s*2 

*λ*<sup>1</sup> =

speckle, and *s*<sup>2</sup> is a heuristically chosen 'stopping level'.

*ω*� <sup>2</sup> ) and eigenvalues (*λ*1, *λ*2) given by:

Gaussian kernel with the structure tensor:

*λ*<sup>1</sup> = *c*1, *λ*<sup>2</sup> =

*δI*(*x*, *y*, *t*)

*<sup>J</sup><sup>ρ</sup>* <sup>=</sup> *<sup>K</sup><sup>ρ</sup>* <sup>∗</sup> (∇*<sup>I</sup>* <sup>∇</sup>*IT*) = *<sup>K</sup><sup>ρ</sup>* <sup>∗</sup> *<sup>I</sup>*<sup>2</sup>

Here, the initial stage of smoothing performed in (12) is not used. As in the CED method, *ρ* is integration scale, the window size over which the orientation information is averaged. The PDE (13) again describes the diffusion, using a diffusion tensor constructed so as to have the

where *α* is a parameter determining the level of smoothing in regions of fully developed

The orientated SRAD (OSRAD) proposed by Krissian *et al.* (Krissian et al., 2007) extended the SRAD method to a tensor diffusion scheme, so diffusion can vary with direction to speckle adaptive diffusion filtering. The improvements of the DPAD method are also used in this method, such as the use of a larger window to estimate *q*(*x*, *y*; *t*), and the median estimation of *q*0(*t*). The OSRAD diffusion function *c*(*q*) is based on the Kuan *et al.* filter, as in (9). It was shown that the local directional variance is related to the local geometry of the image.

, if *<sup>κ</sup>* <sup>≤</sup> *<sup>s</sup>*<sup>2</sup>

where *q*<sup>0</sup> is the 'speckle scale function', a diffusion threshold controlling the level of smoothing, equivalent to the noise variation coefficient *Cn* of the SAR filters.

The work of Aja-Fernandez and Alberola-Lopez (Aja-Fernandez & Alberola-Lopez, 2006) proposed a number of improvements to the SRAD technique, known as detail preserving anisotropic diffusion (DPAD). Noting that (8) is derived from the Lee filter, this is replaced with the following derived from the Kuan filter:

$$\mathcal{L}\left[q(\mathbf{x},\mathbf{y},t),q\_0(t)\right] = \frac{1 + 1/q^2(\mathbf{x},\mathbf{y},t)}{1 + 1/q\_0^2(t)}\tag{9}$$

The second alteration concerns the calculation of the ICOV, showing that (7) is equivalent to the ratio of local standard deviation and mean estimators. In (7), these local estimators were calculated in using the four nearest neighbours of each pixel, while in DPAD a larger neighbourhood is used for more accurate estimates:

$$q(\mathbf{x}, y, t) = \sqrt{\frac{\sigma\_I^2(\mathbf{x}, y, t)}{\overline{I}(\mathbf{x}, y, t)^2}} = \sqrt{\frac{1}{\frac{|\eta\_{\mathbf{x}, y}| - 1}{\overline{I}(\mathbf{x}, y, t)} \sum\_{p \in \eta\_{\mathbf{x}, y}} \left(I\_p - \overline{I}(\mathbf{x}, y, t)\right)^2}{\overline{I}(\mathbf{x}, y, t)^2}}\tag{10}$$

where *<sup>η</sup>x*,*<sup>y</sup>* is a square *<sup>Z</sup>* <sup>×</sup> *<sup>Z</sup>* neighbourhood, and ¯*I*(*x*, *<sup>y</sup>*, *<sup>t</sup>*)=(1/|*ηx*,*y*|) <sup>∑</sup>*p*∈*ηx*,*<sup>y</sup> Ip*. This is shown to be more accurate than the formulation of (7). The third contribution of (Aja-Fernandez & Alberola-Lopez, 2006) related to the estimation of *q*0(*t*), calculated as *median*{*q*(*x*, *y*; *t*)}. This approach requires less computation than the previously proposed method of (Yu & Acton, 2004), and produced similar results.

Tensor valued schemes, proposed by Weickert (Weickert, 1998; 1999), allow the strength of diffusion to vary directionally at each location. Denoted Coherence Enhancing Diffusion (CED), Weickert's method aims to enhance the enhance the smooth curves within an image, such as those often present in medical images. The structure tensor *T* is used to describe the image gradient:

$$T\_{\quad} = \nabla I \otimes \nabla I^T = \begin{pmatrix} I\_x^2 & I\_{xy} \\ I\_{xy} & I\_y^2 \end{pmatrix} \tag{11}$$

where *Ix*, *Iy* are the *x* and *y* gradients of the image: ∇*I* = (*Ix*, *Iy*). To make the gradient description robust to small noise fluctuations, local averaging of the observed image is performed as *I<sup>σ</sup>* = *K<sup>σ</sup>* ∗ *I*, where ∗ represents convolution, and *K<sup>σ</sup>* is a Gaussian kernel of variance *<sup>σ</sup>*2. The gradient <sup>∇</sup>*I<sup>σ</sup>* represents only information from image details larger than *O*(*σ*). Thus *σ* is referred to as the *noise scale*. The structure tensor is formed using a second level of Gaussian smoothing:

$$T\_{\rho} = K\_{\rho} \* \left(\nabla I\_{\sigma} \nabla I\_{\sigma}^{T}\right) = \begin{pmatrix} T\_{11} & T\_{12} \\ T\_{21} & T\_{22} \end{pmatrix} \tag{12}$$

The values of *T<sup>ρ</sup>* then represent image information from a neighbourhood defined by *ρ*, the *integration scale*. While the structure tensor is simply another representation of the image gradient ∇*I*, and contains no more information than ∇*I*, it has the advantage of allowing local averaging as in (12) without cancellation.

8 Will-be-set-by-IN-TECH

where *q*<sup>0</sup> is the 'speckle scale function', a diffusion threshold controlling the level of

The work of Aja-Fernandez and Alberola-Lopez (Aja-Fernandez & Alberola-Lopez, 2006) proposed a number of improvements to the SRAD technique, known as detail preserving anisotropic diffusion (DPAD). Noting that (8) is derived from the Lee filter, this is replaced

*<sup>c</sup>* [*q*(*x*, *<sup>y</sup>*, *<sup>t</sup>*), *<sup>q</sup>*0(*t*)] <sup>=</sup> <sup>1</sup> <sup>+</sup> 1/*q*2(*x*, *<sup>y</sup>*, *<sup>t</sup>*)

The second alteration concerns the calculation of the ICOV, showing that (7) is equivalent to the ratio of local standard deviation and mean estimators. In (7), these local estimators were calculated in using the four nearest neighbours of each pixel, while in DPAD a larger

> 1 <sup>|</sup>*ηx*,*y*| − <sup>1</sup> <sup>∑</sup>

where *<sup>η</sup>x*,*<sup>y</sup>* is a square *<sup>Z</sup>* <sup>×</sup> *<sup>Z</sup>* neighbourhood, and ¯*I*(*x*, *<sup>y</sup>*, *<sup>t</sup>*)=(1/|*ηx*,*y*|) <sup>∑</sup>*p*∈*ηx*,*<sup>y</sup> Ip*. This is shown to be more accurate than the formulation of (7). The third contribution of (Aja-Fernandez & Alberola-Lopez, 2006) related to the estimation of *q*0(*t*), calculated as *median*{*q*(*x*, *y*; *t*)}. This approach requires less computation than the previously proposed

Tensor valued schemes, proposed by Weickert (Weickert, 1998; 1999), allow the strength of diffusion to vary directionally at each location. Denoted Coherence Enhancing Diffusion (CED), Weickert's method aims to enhance the enhance the smooth curves within an image, such as those often present in medical images. The structure tensor *T* is used to describe the

where *Ix*, *Iy* are the *x* and *y* gradients of the image: ∇*I* = (*Ix*, *Iy*). To make the gradient description robust to small noise fluctuations, local averaging of the observed image is performed as *I<sup>σ</sup>* = *K<sup>σ</sup>* ∗ *I*, where ∗ represents convolution, and *K<sup>σ</sup>* is a Gaussian kernel of variance *<sup>σ</sup>*2. The gradient <sup>∇</sup>*I<sup>σ</sup>* represents only information from image details larger than *O*(*σ*). Thus *σ* is referred to as the *noise scale*. The structure tensor is formed using a second

*<sup>σ</sup>* ) =

The values of *T<sup>ρ</sup>* then represent image information from a neighbourhood defined by *ρ*, the *integration scale*. While the structure tensor is simply another representation of the image gradient ∇*I*, and contains no more information than ∇*I*, it has the advantage of allowing

*T*<sup>11</sup> *T*<sup>12</sup> *T*<sup>21</sup> *T*<sup>22</sup>

 *I*<sup>2</sup> *<sup>x</sup> Ixy Ixy I*<sup>2</sup> *y* 

*<sup>T</sup>* <sup>=</sup> <sup>∇</sup>*<sup>I</sup>* ⊗ ∇*I<sup>T</sup>* <sup>=</sup>

*<sup>T</sup><sup>ρ</sup>* <sup>=</sup> *<sup>K</sup><sup>ρ</sup>* <sup>∗</sup> (∇*Iσ*∇*I<sup>T</sup>*

1 + 1/*q*<sup>2</sup>

*p*∈*ηx*,*<sup>y</sup>*

*Ip* <sup>−</sup> ¯*I*(*x*, *<sup>y</sup>*, *<sup>t</sup>*)

<sup>0</sup>(*t*) (9)

2

¯*I*(*x*, *<sup>y</sup>*, *<sup>t</sup>*)<sup>2</sup> (10)

(11)

(12)

smoothing, equivalent to the noise variation coefficient *Cn* of the SAR filters.

with the following derived from the Kuan filter:

neighbourhood is used for more accurate estimates:

 *σ*2 *<sup>I</sup>* (*x*, *y*, *t*) ¯*I*(*x*, *<sup>y</sup>*, *<sup>t</sup>*)<sup>2</sup> <sup>=</sup>

method of (Yu & Acton, 2004), and produced similar results.

*q*(*x*, *y*, *t*) =

image gradient:

level of Gaussian smoothing:

local averaging as in (12) without cancellation.

The eigenvectors of *T<sup>ρ</sup>* are denoted by (*ω*� 1, *ω*� <sup>2</sup>), and the corresponding eigenvalues by (*μ*1, *μ*2). If the eigenvalues are ordered so that *μ*<sup>1</sup> ≥ *μ*2, then (*ω*� 1, *ω*� <sup>2</sup>) give the directions of maximum and minimum local variation, respectively. These are the directions normal and tangent to the local image gradient, the gradient and contour directions. The corresponding eigenvalues give the strength of the gradient in these directions, and also provide information on the local coherence or anisotropy. A measure of local coherence is defined as *<sup>κ</sup>* = (*μ*<sup>1</sup> <sup>−</sup> *<sup>μ</sup>*2)<sup>2</sup> (Weickert, 1999). The CED diffusion process is described by the PDE:

$$\frac{\delta I(\mathbf{x}, y, t)}{\delta t} = \nabla.(D\nabla I(\mathbf{x}, y, t))\tag{13}$$

where *D* is the diffusion matrix, constructed with the same eigenvectors as *T<sup>ρ</sup>* (�*e*<sup>1</sup> = *ω*� 1,�*e*<sup>2</sup> = *ω*� <sup>2</sup> ) and eigenvalues (*λ*1, *λ*2) given by:

$$\begin{array}{rcl} \lambda\_1 &=& c\_1, & \lambda\_2 &=& \begin{cases} c\_1, & \text{if } \mu\_1 = \mu\_2 \\ c\_1 + (1 - c\_1) \exp\left(\frac{-c\_2}{\kappa}\right), & \text{otherwise} \end{cases} \end{array} \tag{14}$$

where *c*<sup>1</sup> and *c*<sup>2</sup> are parameters constrained by 0 < *c*<sup>1</sup> � 1 and *c*<sup>2</sup> > 0.

The nonlinear coherent diffusion (NCD) method of Abd-Elmoniem *et al.* (Abd-Elmoniem et al., 2002) is a tensor valued anisotropic diffusion scheme for the removal of speckle. The eigenvalues of the diffusion tensor define the directional strength of diffusion at each image location, and these are chosen to reflect an estimate of the strength of speckle at that location. Image regions closely resembling fully developed speckle are mean filtered, while those dissimilar remain unaltered. Similar to the CED method, this approach uses a tensor-valued diffusion function, calculated as a component-wise convolution of a Gaussian kernel with the structure tensor:

$$\begin{array}{rcl} J\_{\rho} & = \mathbf{K}\_{\rho} \ast \left( \nabla I \,\nabla I^{T} \right) = \begin{pmatrix} \mathbf{K}\_{\rho} \ast I\_{\mathbf{x}}^{2} & \mathbf{K}\_{\rho} \ast I\_{\mathbf{x}\mathbf{y}} \\ \mathbf{K}\_{\rho} \ast I\_{\mathbf{x}\mathbf{y}} & \mathbf{K}\_{\rho} \ast I\_{\mathbf{y}}^{2} \end{pmatrix} \end{array} \tag{15}$$

Here, the initial stage of smoothing performed in (12) is not used. As in the CED method, *ρ* is integration scale, the window size over which the orientation information is averaged. The PDE (13) again describes the diffusion, using a diffusion tensor constructed so as to have the same eigenvectors as *Jρ*, but with eigenvalues *λ*1, *λ*<sup>2</sup> defined as:

$$
\lambda\_1 \quad = \begin{cases}
\mathfrak{a} \left(1 - \frac{\kappa}{s^2}\right), & \text{if } \kappa \le s^2 \\
0, & \text{otherwise}
\end{cases}, \quad \lambda\_2 \quad = \quad \mathfrak{a} \tag{16}
$$

where *α* is a parameter determining the level of smoothing in regions of fully developed speckle, and *s*<sup>2</sup> is a heuristically chosen 'stopping level'.

The orientated SRAD (OSRAD) proposed by Krissian *et al.* (Krissian et al., 2007) extended the SRAD method to a tensor diffusion scheme, so diffusion can vary with direction to speckle adaptive diffusion filtering. The improvements of the DPAD method are also used in this method, such as the use of a larger window to estimate *q*(*x*, *y*; *t*), and the median estimation of *q*0(*t*). The OSRAD diffusion function *c*(*q*) is based on the Kuan *et al.* filter, as in (9). It was shown that the local directional variance is related to the local geometry of the image.

Trends and Perceptions 11

Speckle Reduction in Echocardiography: Trends and Perceptions 51

where *v* ∈ [−1, 1] represents each wavelet coefficient, and the three thresholds are related as 0 ≤ *T*<sup>1</sup> ≤ *T*<sup>2</sup> ≤ *T*<sup>3</sup> ≤ 1. The value of *u*¯ is determined according to *u*¯ = *a*(*T*<sup>3</sup> −

Noise removal in the wavelet domain is also performed using Bayesian denoising techniques, which model the distributions of the wavelet coefficients. This a priori information is used to infer the noise free coefficients. Gupta *et al.* (Gupta et al., 2005) modelled the wavelet coefficients of the underlying speckle free image using a generalised Laplacian distribution, simultaneously removing speckle and performing compression using a quantisation function.

of a symmetric *α* stable (S*α*S) distribution (as *R*(*i*, *j*)), and a zero mean Gaussian distribution for *n*(*i*, *j*). The variance of the Gaussian noise is estimated using the median absolute deviation (MAD) method, while the parameters of the S*α*S distribution are estimated by least squares fitting of the observed density function spectrum to the empirical characteristic function. After estimation of the parameters of the statistical model, a shrinkage function is found by numerical calculation of the maximum a posteriori (MAP) estimation curve. The wavelet coefficients are modified by the shrinkage function, and the inverse wavelet transform

The technique of Rabani *et al.* (Rabbani et al., 2008) models the distribution of the noise free wavelet coefficients using a local mixture of either Gaussian or Laplacian distributions. The speckle noise is assumed to be either Gaussian or Rayleigh in nature. For all combinations of local mixture distributions and speckle noise distributions, both the MAP and minimum mean squared error (MMSE) estimators are derived analytically. A recently proposed method by Fu *et al.* (Fu et al., 2010) accomplishes bivariate shrinkage of the wavelet coefficients. This approach models the joint density of the coefficients in each scale with their parents in the

The third type of wavelet noise removal uses the correlation of useful wavelet coefficients across scales (Pižurica et al., 2003). This technique does not rely on a model for the image noise, but rather locates the signals of interest based on their interscale persistence. This initial classification step is followed by empirical estimates of the signal and noise probability density functions (PDFs). These are used to define a shrinkage map which suppress those

The NMWD method (Yue et al., 2006) aims to combine wavelet analysis with anisotropic diffusion. Wavelet based signal/noise discrimination is employed to overcome the

0, if |*v*| < *T*<sup>1</sup> *sign*(*v*)*T*<sup>2</sup> + *u*¯, if *T*<sup>2</sup> ≤ |*v*| ≤ *T*<sup>3</sup>

(19)

1, otherwise

, *<sup>a</sup>* <sup>=</sup> <sup>1</sup>

*<sup>f</sup>* [*c*(<sup>1</sup> <sup>−</sup> *<sup>b</sup>*)]<sup>−</sup> *<sup>f</sup>* [−*c*(<sup>1</sup> <sup>+</sup> *<sup>b</sup>*)] (20)

(*i*, *j*) as the convolution

*E*(*v*) =

*<sup>u</sup>* <sup>=</sup> *sign*(*v*)(|*v*| − *<sup>T</sup>*2) *T*<sup>3</sup> − *T*<sup>2</sup>

This function adapts to the estimated level of speckle.

produces the denoised image.

wavelet coefficients resulting from noise.

next coarser scale.

⎧ ⎪⎨

⎪⎩

Thus the operator *E*(*v*) is dependant on five parameters: *b*, *c*, *T*1, *T*2, *T*3.

Achim *et al.* (Achim et al., 2001) modelled the wavelet coefficients of *I<sup>l</sup>*

*T*2){ *f* [*c*(*u* − *b*)] − *f* [−*c*(*u* + *b*)]}. The sigmoid function is represented by *f* , and

This method can be implemented by the use of the structure tensor, as in (Weickert, 1999) and (Abd-Elmoniem et al., 2002), or by using the Hessian matrix as in (Krissian, 2002). In the 2-D case, (*ω* 1, *ω* <sup>2</sup>) are the eigenvectors of *T<sup>ρ</sup>* from (12), and are used as the basis of the diffusion matrix, *D*. The eigenvalues of *D*, which determine the strength of diffusion in the gradient and curvature directions, are given as:

$$
\lambda\_1 \quad = \mathfrak{c}\_{\text{rad}} \quad , \quad \lambda\_2 \quad = \mathfrak{c}\_{\text{tang}} \tag{17}
$$

Where *csrad* is the SRAD diffusion (*c*(*q*)), and *ctang* is a constant. Diffusion is then performed as per (13).

#### **3.2.3 Multiscale methods**

Multiscale methods are common in image processing, and both the wavelet and pyramid (Burt & Adelson, 1983) transforms have been employed in the reduction of speckle. The well-known wavelet transform isolates local frequency subbands using a quadrature mirror pair of filters. The the pyramid transform does not require quadrature filters. More details on this method can be found in (Adelson et al., 1984).

Wavelet techniques can be grouped into those which operate by thresholding, Bayesian estimation, or correlation between coefficients. Many techniques use the soft thresholding approach of Donoho (Donoho, 1995), of which some of the first adoptions for speckle were proposed by (Guo et al., 1994) and (Moulin, 1993). These methods use a logarithmic transformation to allow treatment of the speckle as additive. The thresholding method of (Hao et al., 1999) operates on the output of the AWMF filter. The difference image between the AMWF output and the original image contains the high frequency information removed by the AWMF. Both images have speckle removed by soft thresholding in the wavelet domain, and after reconstruction the two images are summed together.

Using a multiplicative model for a speckled image, the method of Zong *et al.* (Zong et al., 1998) applies logarithmic and wavelet transforms as:

$$\begin{aligned} I(i,j) &= \mathbb{R}(i,j)n(i,j) \\ I^l(i,j) &= \mathbb{R}^l(i,j) + n^l(i,j) \\ W[I(i,j)] &= \{ (W\_k^d[I(i,j)]) \}\_{1 \le k \le l'}^{d=1,2} S\_K[I(i,j)] \} \end{aligned} \tag{18}$$

where *R* and *n* are the speckle free and speckle noise components, (*i*, *j*) are the pixel indecies, and *I<sup>l</sup>* = *log*(*I*). Here *n<sup>l</sup>* (*i*, *j*) is approximated as additive white noise. The *K*-level discrete Dyadic Wavelet Transform (DWT) of (Mallat & Zhong, 1992) generates *W<sup>d</sup> <sup>k</sup>* {*I*(*i*, *j*)}, the set of wavelet coefficients at scale 2*<sup>k</sup>* (level *k*) and spatial orientation *d* (*d* = 1 for horizontal and *d* = 2 for vertical). The approximation coefficients at the coarsest scale *K* are denoted by *SK*{*I*(*i*, *j*)}. Soft thresholding is applied to the finer scales (levels one and two), with coefficient dependent thresholds.

A nonlinear function is applied to the other, coarser, scales. This incorporates hard thresholding and a nonlinear contrast enhancement term:

10 Will-be-set-by-IN-TECH

This method can be implemented by the use of the structure tensor, as in (Weickert, 1999) and (Abd-Elmoniem et al., 2002), or by using the Hessian matrix as in (Krissian, 2002). In the 2-D case, (*ω* 1, *ω* <sup>2</sup>) are the eigenvectors of *T<sup>ρ</sup>* from (12), and are used as the basis of the diffusion matrix, *D*. The eigenvalues of *D*, which determine the strength of diffusion in the gradient

Where *csrad* is the SRAD diffusion (*c*(*q*)), and *ctang* is a constant. Diffusion is then performed

Multiscale methods are common in image processing, and both the wavelet and pyramid (Burt & Adelson, 1983) transforms have been employed in the reduction of speckle. The well-known wavelet transform isolates local frequency subbands using a quadrature mirror pair of filters. The the pyramid transform does not require quadrature filters. More details on

Wavelet techniques can be grouped into those which operate by thresholding, Bayesian estimation, or correlation between coefficients. Many techniques use the soft thresholding approach of Donoho (Donoho, 1995), of which some of the first adoptions for speckle were proposed by (Guo et al., 1994) and (Moulin, 1993). These methods use a logarithmic transformation to allow treatment of the speckle as additive. The thresholding method of (Hao et al., 1999) operates on the output of the AWMF filter. The difference image between the AMWF output and the original image contains the high frequency information removed by the AWMF. Both images have speckle removed by soft thresholding in the wavelet domain,

Using a multiplicative model for a speckled image, the method of Zong *et al.* (Zong et al.,

(*i*, *j*)

1≤*k*≤*J*

,*SK*[*I*(*i*, *j*)]}

(*i*, *j*) is approximated as additive white noise. The *K*-level discrete

(18)

*<sup>k</sup>* {*I*(*i*, *j*)}, the set of

*<sup>k</sup>* [*I*(*i*, *<sup>j</sup>*)])*d*=1,2

where *R* and *n* are the speckle free and speckle noise components, (*i*, *j*) are the pixel indecies,

wavelet coefficients at scale 2*<sup>k</sup>* (level *k*) and spatial orientation *d* (*d* = 1 for horizontal and *d* = 2 for vertical). The approximation coefficients at the coarsest scale *K* are denoted by *SK*{*I*(*i*, *j*)}. Soft thresholding is applied to the finer scales (levels one and two), with coefficient dependent

A nonlinear function is applied to the other, coarser, scales. This incorporates hard

(*i*, *j*) + *n<sup>l</sup>*

*I*(*i*, *j*) =*R*(*i*, *j*)*n*(*i*, *j*)

(*i*, *j*) =*R<sup>l</sup>*

*<sup>W</sup>*[*I*(*i*, *<sup>j</sup>*)]={(*W<sup>d</sup>*

Dyadic Wavelet Transform (DWT) of (Mallat & Zhong, 1992) generates *W<sup>d</sup>*

*λ*<sup>1</sup> = *csrad* , *λ*<sup>2</sup> = *ctang* (17)

and curvature directions, are given as:

this method can be found in (Adelson et al., 1984).

and after reconstruction the two images are summed together.

1998) applies logarithmic and wavelet transforms as:

*I l*

thresholding and a nonlinear contrast enhancement term:

as per (13).

**3.2.3 Multiscale methods**

and *I<sup>l</sup>* = *log*(*I*). Here *n<sup>l</sup>*

thresholds.

$$E(v) \quad = \begin{cases} 0, & \text{if} \quad |v| < T\_1 \\ \text{sign}(v)T\_2 + \bar{u}, & \text{if} \quad T\_2 \le |v| \le T\_3 \\ 1, & \text{otherwise} \end{cases} \tag{19}$$

where *v* ∈ [−1, 1] represents each wavelet coefficient, and the three thresholds are related as 0 ≤ *T*<sup>1</sup> ≤ *T*<sup>2</sup> ≤ *T*<sup>3</sup> ≤ 1. The value of *u*¯ is determined according to *u*¯ = *a*(*T*<sup>3</sup> − *T*2){ *f* [*c*(*u* − *b*)] − *f* [−*c*(*u* + *b*)]}. The sigmoid function is represented by *f* , and

$$u = \frac{\text{sign}(v)(|v| - T\_2)}{T\_3 - T\_2}, \quad a = \frac{1}{f\left[c(1-b)\right] - f\left[-c(1+b)\right]}\tag{20}$$

Thus the operator *E*(*v*) is dependant on five parameters: *b*, *c*, *T*1, *T*2, *T*3.

Noise removal in the wavelet domain is also performed using Bayesian denoising techniques, which model the distributions of the wavelet coefficients. This a priori information is used to infer the noise free coefficients. Gupta *et al.* (Gupta et al., 2005) modelled the wavelet coefficients of the underlying speckle free image using a generalised Laplacian distribution, simultaneously removing speckle and performing compression using a quantisation function. This function adapts to the estimated level of speckle.

Achim *et al.* (Achim et al., 2001) modelled the wavelet coefficients of *I<sup>l</sup>* (*i*, *j*) as the convolution of a symmetric *α* stable (S*α*S) distribution (as *R*(*i*, *j*)), and a zero mean Gaussian distribution for *n*(*i*, *j*). The variance of the Gaussian noise is estimated using the median absolute deviation (MAD) method, while the parameters of the S*α*S distribution are estimated by least squares fitting of the observed density function spectrum to the empirical characteristic function. After estimation of the parameters of the statistical model, a shrinkage function is found by numerical calculation of the maximum a posteriori (MAP) estimation curve. The wavelet coefficients are modified by the shrinkage function, and the inverse wavelet transform produces the denoised image.

The technique of Rabani *et al.* (Rabbani et al., 2008) models the distribution of the noise free wavelet coefficients using a local mixture of either Gaussian or Laplacian distributions. The speckle noise is assumed to be either Gaussian or Rayleigh in nature. For all combinations of local mixture distributions and speckle noise distributions, both the MAP and minimum mean squared error (MMSE) estimators are derived analytically. A recently proposed method by Fu *et al.* (Fu et al., 2010) accomplishes bivariate shrinkage of the wavelet coefficients. This approach models the joint density of the coefficients in each scale with their parents in the next coarser scale.

The third type of wavelet noise removal uses the correlation of useful wavelet coefficients across scales (Pižurica et al., 2003). This technique does not rely on a model for the image noise, but rather locates the signals of interest based on their interscale persistence. This initial classification step is followed by empirical estimates of the signal and noise probability density functions (PDFs). These are used to define a shrinkage map which suppress those wavelet coefficients resulting from noise.

The NMWD method (Yue et al., 2006) aims to combine wavelet analysis with anisotropic diffusion. Wavelet based signal/noise discrimination is employed to overcome the

Trends and Perceptions 13

Speckle Reduction in Echocardiography: Trends and Perceptions 53

The majority of the papers proposing these filters contain a comparison of the proposed method with some others from the literature. Common techniques for evaluating relative performance are quantitative image quality metrics, and qualitative inspection, often by the authors themselves. Test data for evaluation includes clinical and phantom images, as well as simulated ultrasound which allows evaluation of filtering relative to an ideal speckle free reference. A select number of independent reviews have also been published, which vary in

Thakur and Anand (Thakur & Anand, 2005) compared the suitability of a number of different wavelets for the reduction of speckle in ultrasound imagery. Adam *et al.* (Adam et al., 2006) looked at the effect of a combination of spatial compounding and postacquisition filtering. Different methods of compounding these images were evaluated in this work, in combination with a number of postacquisition filters. These were applied to simulated kidney images generated using the Field II software package (Jensen, 1996). It was shown that postacquisition filtering improved the images to a greater degree than compounding alone, and that the SRAD filter was the better of the two considered. A recent comparison by Mateo and Fernández-Caballero (Mateo & Fernández-Caballero, 2009) evaluated median filtering, the AWMF filter, two low-pass filters, and a simple wavelet filter. Lowpass filtering with the Butterworth filter was deemed by the authors to be the best of the methods considered. A comprehensive comparison of a large number of speckle reduction filters for application to clinical carotid ultrasonography was presented by Loizou *et al.* (Loizou et al., 2005). Evaluation was performed both by automated analysis, and also using classification by experts. In both cases, the focus was on the diagnosis of atherosclerosis (thickened artery walls due to plaque deposit). A set of clinical images from patients deemed to be at risk of this condition was used in filter evaluation, and these were divided into a symptomatic set (from patients who have displayed symptoms of this condition, such as stroke incidents), and an symptomatic set. For the test by automated analysis, 440 images were used, divided equally between the two sets. Automated analysis proceeded by calculating a large number (56) of texture features for each filtered image. The level of separability between the symptomatic and symptomatic sets was then analysed using a number of approaches, using a distance metric an the statistical Wilcoxon rank sum test. A set of image quality metrics were also applied, comparing the filtered image to the unfiltered version in each case. The expert test was performed with 100 images, split evenly between symptomatic and symptomatic groups. The filtered and unfiltered images were shown to two experts at random, and each expert rates the quality of the image on a scale of one to five. Only one method (the Geometric filter) was seen to improve the image quality as perceived by both experts across the entire dataset. A difference in the evaluations between the experts was noted, although this was not investigated statistically. The authors accounted for this by reference to the differing clinical

The present author conducted and reported on a study which compared clinical and computational evaluation of speckle filtering in echocardiographic images (Finn et al., 2009). Subjective visual assessment was performed by a group of six clinical experts, all of whom are experienced cardiac physicians or technicians. The majority of the evaluation strategies described in the literature review of the previous chapter report results of visual inspection by the authors themselves, rather than the opinion of clinical experts (exception include (Loizou et al., 2005; Zong et al., 1998)). The basic qualities which are generally held to

the nature and depth of the investigation performed.

specialities of the experts.

shortcomings of the image gradient (as used in the PMAD, CED and NCD methods) for discrimination in speckled images. The gradient cannot always precisely separate the image and noise in ultrasound images, as variations due to speckle noise may be larger than those corresponding to underlying image (Yue et al., 2006). The image is decomposed using the DWT of Mallat and Zhong, as in the Zong *et al.* method. The modulus of the wavelet coefficients at each scale is defined as:

$$M\_k\{I(i,j)\} = \sqrt{\sum\_{d=1}^2 \left|\mathcal{W}\_k^d\{I(i,j)\}\right|\_{k=1,2,\ldots,K}^2} \tag{21}$$

The normalised wavelet modulus was found to be large in edge-related regions and small for noise and texture, and so is used for signal/noise discrimination in this method. For amplitude images the wavelet modulus is normalised by:

$$
\tilde{M}\_k I = \frac{M\_k \{ I(i, j) \}}{\mu\_Z}, \quad k = 1, 2, \dots, K \tag{22}
$$

Here *<sup>μ</sup><sup>Z</sup>* is a local mean calculated using a widow size *<sup>Z</sup>* <sup>×</sup> *<sup>Z</sup>*. The histogram of *<sup>M</sup>*˜ *<sup>k</sup> <sup>I</sup>* is modelled as a Rayleigh mixture distribution, composed of the sum of edge and noise pixels as:

$$
\tilde{M}\_k I \simeq n\_k p\_{n,k}(\mathbf{x}, \lambda\_n) + (1 - n\_k) p\_{\varepsilon,k}(\mathbf{x}, \lambda\_\varepsilon) \tag{23}
$$

where *pn*,*<sup>k</sup>* is a Rayleigh distribution with parameter *λn*, representing the noise pixels. Similarly, *pe*,*<sup>k</sup>* are the edge pixels, Rayleigh distributed with parameter *λe*. The proportion of the mixture distribution resulting from noise-related values is given as *nk*. The parameters of the normalised modulus distribution (*σn*,*k*, *σe*,*<sup>k</sup>* and *nk*) are estimated using the Expectation-Maximisation (EM) method (Dempster et al., 1977). These parameters are used to determine the strength of n anisotropic diffusion process. After diffusion, the wavelet coefficients are used the synthesize the speckle reduced image. This process is repeated for a number of iterations.

As well as wavelet based methods, multiresolution pyramid methods of speckle reduction have been proposed. The approach of Aiazzi *et al.* (Aiazzi et al., 1998) extends the approach of the Kuan filter to process each layer in the multiscale pyramid decomposition. Sattar *et al.* (Sattar et al., 1997) presented a method which both reduces speckle and enhances image edges. Multiscale decomposition is performed using a pyramid transform. An edge detector is applied to the lowpass image, the output of which determines the coefficients from the high pass image which are included in reconstruction. The success of this method is therefore dependant on accurate operation of the edge detector, and a number of different techniques are tested.

The approach of Zhang *et al.* (Zhang et al., 2007) combines the approaches of multiscale analysis and anisotropic diffusion, and so is similar in approach to the NMWD method above.

#### **4. Evaluation of speckle reduction**

As shown above, a large variety of speckle reduction filters have been proposed. Evaluating the relative performance of these filters has been performed by a number of different methods. 12 Will-be-set-by-IN-TECH

shortcomings of the image gradient (as used in the PMAD, CED and NCD methods) for discrimination in speckled images. The gradient cannot always precisely separate the image and noise in ultrasound images, as variations due to speckle noise may be larger than those corresponding to underlying image (Yue et al., 2006). The image is decomposed using the DWT of Mallat and Zhong, as in the Zong *et al.* method. The modulus of the wavelet

The normalised wavelet modulus was found to be large in edge-related regions and small for noise and texture, and so is used for signal/noise discrimination in this method. For

Here *<sup>μ</sup><sup>Z</sup>* is a local mean calculated using a widow size *<sup>Z</sup>* <sup>×</sup> *<sup>Z</sup>*. The histogram of *<sup>M</sup>*˜ *<sup>k</sup> <sup>I</sup>* is modelled as a Rayleigh mixture distribution, composed of the sum of edge and noise pixels

where *pn*,*<sup>k</sup>* is a Rayleigh distribution with parameter *λn*, representing the noise pixels. Similarly, *pe*,*<sup>k</sup>* are the edge pixels, Rayleigh distributed with parameter *λe*. The proportion of the mixture distribution resulting from noise-related values is given as *nk*. The parameters of the normalised modulus distribution (*σn*,*k*, *σe*,*<sup>k</sup>* and *nk*) are estimated using the Expectation-Maximisation (EM) method (Dempster et al., 1977). These parameters are used to determine the strength of n anisotropic diffusion process. After diffusion, the wavelet coefficients are used the synthesize the speckle reduced image. This process is repeated for a

As well as wavelet based methods, multiresolution pyramid methods of speckle reduction have been proposed. The approach of Aiazzi *et al.* (Aiazzi et al., 1998) extends the approach of the Kuan filter to process each layer in the multiscale pyramid decomposition. Sattar *et al.* (Sattar et al., 1997) presented a method which both reduces speckle and enhances image edges. Multiscale decomposition is performed using a pyramid transform. An edge detector is applied to the lowpass image, the output of which determines the coefficients from the high pass image which are included in reconstruction. The success of this method is therefore dependant on accurate operation of the edge detector, and a number of different techniques

The approach of Zhang *et al.* (Zhang et al., 2007) combines the approaches of multiscale analysis and anisotropic diffusion, and so is similar in approach to the NMWD method above.

As shown above, a large variety of speckle reduction filters have been proposed. Evaluating the relative performance of these filters has been performed by a number of different methods.

*<sup>k</sup>* {*I*(*i*, *<sup>j</sup>*)}|<sup>2</sup>

*<sup>M</sup>*˜ *<sup>k</sup> <sup>I</sup>* � *nkpn*,*k*(*x*, *<sup>λ</sup>n*)+(<sup>1</sup> <sup>−</sup> *nk*)*pe*,*k*(*x*, *<sup>λ</sup>e*) (23)

*<sup>k</sup>*=1,2,..,*<sup>K</sup>* (21)

, *k* = 1, 2, .., *K* (22)

 2 ∑ *d*=1 <sup>|</sup>*W<sup>d</sup>*

*<sup>M</sup>*˜ *<sup>k</sup> <sup>I</sup>* <sup>=</sup> *Mk*{*I*(*i*, *<sup>j</sup>*)} *μZ*

coefficients at each scale is defined as:

as:

number of iterations.

are tested.

**4. Evaluation of speckle reduction**

*Mk*{*I*(*i*, *j*)} =

amplitude images the wavelet modulus is normalised by:

The majority of the papers proposing these filters contain a comparison of the proposed method with some others from the literature. Common techniques for evaluating relative performance are quantitative image quality metrics, and qualitative inspection, often by the authors themselves. Test data for evaluation includes clinical and phantom images, as well as simulated ultrasound which allows evaluation of filtering relative to an ideal speckle free reference. A select number of independent reviews have also been published, which vary in the nature and depth of the investigation performed.

Thakur and Anand (Thakur & Anand, 2005) compared the suitability of a number of different wavelets for the reduction of speckle in ultrasound imagery. Adam *et al.* (Adam et al., 2006) looked at the effect of a combination of spatial compounding and postacquisition filtering. Different methods of compounding these images were evaluated in this work, in combination with a number of postacquisition filters. These were applied to simulated kidney images generated using the Field II software package (Jensen, 1996). It was shown that postacquisition filtering improved the images to a greater degree than compounding alone, and that the SRAD filter was the better of the two considered. A recent comparison by Mateo and Fernández-Caballero (Mateo & Fernández-Caballero, 2009) evaluated median filtering, the AWMF filter, two low-pass filters, and a simple wavelet filter. Lowpass filtering with the Butterworth filter was deemed by the authors to be the best of the methods considered. A comprehensive comparison of a large number of speckle reduction filters for application to clinical carotid ultrasonography was presented by Loizou *et al.* (Loizou et al., 2005). Evaluation was performed both by automated analysis, and also using classification by experts. In both cases, the focus was on the diagnosis of atherosclerosis (thickened artery walls due to plaque deposit). A set of clinical images from patients deemed to be at risk of this condition was used in filter evaluation, and these were divided into a symptomatic set (from patients who have displayed symptoms of this condition, such as stroke incidents), and an symptomatic set. For the test by automated analysis, 440 images were used, divided equally between the two sets. Automated analysis proceeded by calculating a large number (56) of texture features for each filtered image. The level of separability between the symptomatic and symptomatic sets was then analysed using a number of approaches, using a distance metric an the statistical Wilcoxon rank sum test. A set of image quality metrics were also applied, comparing the filtered image to the unfiltered version in each case. The expert test was performed with 100 images, split evenly between symptomatic and symptomatic groups. The filtered and unfiltered images were shown to two experts at random, and each expert rates the quality of the image on a scale of one to five. Only one method (the Geometric filter) was seen to improve the image quality as perceived by both experts across the entire dataset. A difference in the evaluations between the experts was noted, although this was not investigated statistically. The authors accounted for this by reference to the differing clinical specialities of the experts.

The present author conducted and reported on a study which compared clinical and computational evaluation of speckle filtering in echocardiographic images (Finn et al., 2009). Subjective visual assessment was performed by a group of six clinical experts, all of whom are experienced cardiac physicians or technicians. The majority of the evaluation strategies described in the literature review of the previous chapter report results of visual inspection by the authors themselves, rather than the opinion of clinical experts (exception include (Loizou et al., 2005; Zong et al., 1998)). The basic qualities which are generally held to

Trends and Perceptions 15

Speckle Reduction in Echocardiography: Trends and Perceptions 55

3. If there were significant relationships between the subjective expert scores and the image

The expert scores are an ordinal categorical data set, and so the non-parametric Kruskal-Wallis test (Kruskal & Wallis, 1953) was used to investigate inter-expert differences. For the second and third analyses above, correlations were quantified using Spearman's rank correlation coefficient (*ρ*) (Spearman, 1904). All tests were performed using the SPSS software package,

Filtering resulted in a reduction in perceived Speckle Level in almost two thirds of cases. However, the aggregate Overall Quality and Detail Clarity scores were negative in over half of cases, indicating that the experts did not view speckle reduction as beneficial for manual analysis. This is in general agreement with the results of Loizou *et al.* (Loizou et al., 2005). The results of Dantas and Costa (Dantas & Costa, 2007) appear to be relevant: while speckle reduction does not necessarily lead to a loss of clarity, it does remove 'false-fine' structures (spurious fine detail, beyond the scanning resolution). While these details do not represent tissue structure, its removal can lead to a perceived reduction in sharpness. The assessment

The Kruskal-Wallis test resulted in no no statistically significant differences between the experts in the Overall Quality scores at a 1% level of significance, but that a significant difference exists between experts in both the Speckle Level and Detail Clarity scores. For all of the experts, the relationship between Overall Quality and Detail Clarity is strongly positive and statistically significant. The *ρ* values for the relationship between Overall Quality and Speckle Level show positive relationships in all cases, but is only significant at the 1% level for four of the six experts. The relationship between the Detail Clarity and Speckle Level scores again indicate a positive relationship, and are significant for all but one of the experts. The relationship between the expert scores and the objective image quality metrics is shown

**Pratt's Figure of Merit (FoM) (Pratt, 1977)** measures edge pixel displacement between each

where *Nfilt* and *Norig* are the number edge pixels in edge maps of *Ifilt* and *Iorig*. Parameter

detected edge pixel and the nearest ideal edge pixel. The FoM metric measures how well the edges are preserved through out the filtering process. This metric is shown to have a significant relationship with the Overall Quality expert score at the 1% significance level.

**Mean Squared Error (MSE)** The MSE measures the average absolute difference between two

*Y* ∑ *i*=1

*X* ∑ *j*=1

*max*(*Nfilt*, *Norig*)

*N*ˆ ∑ *i*=1

<sup>9</sup> (Yu & Acton, 2002), and *di* is the Euclidean distance between the *i*

1 1 + *d*<sup>2</sup> *i α*

(*Ifilt*(*i*, *<sup>j</sup>*) <sup>−</sup> *Iorig*(*i*, *<sup>j</sup>*))<sup>2</sup> (25)

(24)

*th*

*FoM*(*Ifilt*, *Iorig*) = <sup>1</sup>

the original and filtered images (average intensity change due to filtering):

*XY*

*MSE*(*Ifilt*, *Iorig*) = <sup>1</sup>

and the level of significance was chosen as 1% (*p* = 0.01) throughout.

of the experts here was not universally negative however.

in Table 1 to be significant for three metrics:

filtered image *Ifilt* and the original image *Iorig*:

*α* is set to a constant <sup>1</sup>

quality metrics.

constitute favourable speckle filtering (homogeneous variance reduction, mean intensity preservation and edge preservation) can be readily determined visually, and do not require clinical expertise or training. However, the assessment of clinical images for diagnostic purposes does require such training and expertise. This study explored the clinical opinion of the quality of speckle filtered echocardiographic images, as judged by experts in the field. A large set of speckle filtered echocardiographic videos were produced by application of a number of speckle reduction filters: The SRAD filter (Yu & Acton, 2002), the NCD filter (Abd-Elmoniem et al., 2002), and the GLM filter proposed by Pižurica *et al.*. Example echocardiographic images processed by these filters are displayed in Fig. 2. A total set of forty eight filtered videos were produced in this fashion, showing differing levels of speckle reduction and image characteristics.

The clinical experts assessed subjective video quality in three criteria, chosen based on the opinion of a senior clinical expert of important clinical factors:

**Speckle Level** The expert's assessment of the level of speckle in each video.

**Detail Clarity** Quantifies the subjective resolvability of diagnostically important details.

**Overall Quality** This quantifies the overall quality of the video, including any other clinical considerations not covered by the other criteria.

A large set of quantitative image quality metrics, commonly used in the literature for evaluation of speckle reduction, were also applied. Statistical analysis was performed in order to determine:


Fig. 2. Example frame from an echocardiographic video, from the long axis view. (a) Unfiltered, (b) SRAD, (c) NCD, (d) GLM, (e) NMWD.

14 Will-be-set-by-IN-TECH

constitute favourable speckle filtering (homogeneous variance reduction, mean intensity preservation and edge preservation) can be readily determined visually, and do not require clinical expertise or training. However, the assessment of clinical images for diagnostic purposes does require such training and expertise. This study explored the clinical opinion of the quality of speckle filtered echocardiographic images, as judged by experts in the field. A large set of speckle filtered echocardiographic videos were produced by application of a number of speckle reduction filters: The SRAD filter (Yu & Acton, 2002), the NCD filter (Abd-Elmoniem et al., 2002), and the GLM filter proposed by Pižurica *et al.*. Example echocardiographic images processed by these filters are displayed in Fig. 2. A total set of forty eight filtered videos were produced in this fashion, showing differing levels of speckle

The clinical experts assessed subjective video quality in three criteria, chosen based on the

A large set of quantitative image quality metrics, commonly used in the literature for evaluation of speckle reduction, were also applied. Statistical analysis was performed in order

2. If there were any statistically significant relationships between the three scoring categories

(a) (b) (c)

(d) (e)

Fig. 2. Example frame from an echocardiographic video, from the long axis view. (a)

Unfiltered, (b) SRAD, (c) NCD, (d) GLM, (e) NMWD.

**Detail Clarity** Quantifies the subjective resolvability of diagnostically important details. **Overall Quality** This quantifies the overall quality of the video, including any other clinical

reduction and image characteristics.

to determine:

for each expert.

opinion of a senior clinical expert of important clinical factors:

considerations not covered by the other criteria.

**Speckle Level** The expert's assessment of the level of speckle in each video.

1. If there were any significant differences between the expert scores

3. If there were significant relationships between the subjective expert scores and the image quality metrics.

The expert scores are an ordinal categorical data set, and so the non-parametric Kruskal-Wallis test (Kruskal & Wallis, 1953) was used to investigate inter-expert differences. For the second and third analyses above, correlations were quantified using Spearman's rank correlation coefficient (*ρ*) (Spearman, 1904). All tests were performed using the SPSS software package, and the level of significance was chosen as 1% (*p* = 0.01) throughout.

Filtering resulted in a reduction in perceived Speckle Level in almost two thirds of cases. However, the aggregate Overall Quality and Detail Clarity scores were negative in over half of cases, indicating that the experts did not view speckle reduction as beneficial for manual analysis. This is in general agreement with the results of Loizou *et al.* (Loizou et al., 2005). The results of Dantas and Costa (Dantas & Costa, 2007) appear to be relevant: while speckle reduction does not necessarily lead to a loss of clarity, it does remove 'false-fine' structures (spurious fine detail, beyond the scanning resolution). While these details do not represent tissue structure, its removal can lead to a perceived reduction in sharpness. The assessment of the experts here was not universally negative however.

The Kruskal-Wallis test resulted in no no statistically significant differences between the experts in the Overall Quality scores at a 1% level of significance, but that a significant difference exists between experts in both the Speckle Level and Detail Clarity scores. For all of the experts, the relationship between Overall Quality and Detail Clarity is strongly positive and statistically significant. The *ρ* values for the relationship between Overall Quality and Speckle Level show positive relationships in all cases, but is only significant at the 1% level for four of the six experts. The relationship between the Detail Clarity and Speckle Level scores again indicate a positive relationship, and are significant for all but one of the experts.

The relationship between the expert scores and the objective image quality metrics is shown in Table 1 to be significant for three metrics:

**Pratt's Figure of Merit (FoM) (Pratt, 1977)** measures edge pixel displacement between each filtered image *Ifilt* and the original image *Iorig*:

$$FoM(I\_{fill\prime}, I\_{orig}) = \frac{1}{\max\{N\_{fill\prime}, N\_{orig}\}} \sum\_{i=1}^{\hat{N}} \frac{1}{1 + d\_i^2 \alpha} \tag{24}$$

where *Nfilt* and *Norig* are the number edge pixels in edge maps of *Ifilt* and *Iorig*. Parameter *α* is set to a constant <sup>1</sup> <sup>9</sup> (Yu & Acton, 2002), and *di* is the Euclidean distance between the *i th* detected edge pixel and the nearest ideal edge pixel. The FoM metric measures how well the edges are preserved through out the filtering process. This metric is shown to have a significant relationship with the Overall Quality expert score at the 1% significance level.

**Mean Squared Error (MSE)** The MSE measures the average absolute difference between two the original and filtered images (average intensity change due to filtering):

$$MSE(I\_{fill\prime}, I\_{orig}) = \frac{1}{XY} \sum\_{i=1}^{Y} \sum\_{j=1}^{X} (I\_{fill}(i, j) - I\_{orig}(i, j))^2 \tag{25}$$

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Speckle Reduction in Echocardiography: Trends and Perceptions 57

(a) (b) (c)

Fig. 3. Example simulated ultrasound image. (a) Echomap, (b) Speckled amplitude image, (c)

Various approaches of varying simplicity have been employed in the literature to produce simulated images (Achim et al., 2001; Sattar et al., 1997; Yu & Acton, 2002). Ultrasound imaging can be treated as a linear process (Jensen, 1991; Ng et al., 2006), i.e. the filtering of an echogenicity map with a point spread function (PSF). An axially-varying PSF was used in (Ng et al., 2007), approximated as piecewise constant, similar to (Michailovich & Adam, 2005). This approach was also employed here, with PSFs at various depths generated using the Field

While the PSF models the imaging system, the imaged medium is modelled as an echogenicity map *h*(*x*, *y*) composed of complex point scatterers, similar to (Dantas & Costa, 2007). Scatterers are positioned randomly within regions of varying density. The phase values of the scatterers follows a uniform distribution, varying from 0 → 2*π* rad, while scatterer magnitude follows a Gaussian distribution with unity mean and *σ* = 0.1. Fig. 3(a) shows an example of an echomap with two regions of differing scatterer densities, with density values of 40% and 10%. Echogenicity maps are filtered to generate a simulated image as *RF*(*x*, *y*) = *h*(*x*, *y*) ∗ *p*(*x*, *y*), *I*(*x*, *y*) = |*RF*(*x*, *y*)|. where *p* is the analytic form of the PSF function at the correct depth, and ∗ denotes convolution. Examples of the granular speckle

The Maximum Writing (MW) technique (Burckhardt, 1978) is used to generate a maximally speckle free version of each of the twenty simulated images. The above convolution is performed multiple times, randomly varying scatterer phase. This produces a series of images with the same structure but differing speckle patterns, the maximum of which is the speckle free image: *IMW* <sup>=</sup> max{|*p*(*x*, *<sup>y</sup>*) <sup>∗</sup> (|*h*(*x*, *<sup>y</sup>*)<sup>|</sup> exp[*φn*])|} (*φ<sup>n</sup>* is the phase of the *<sup>n</sup>th* set of scatterers generated). In practice, this technique is applied until the contribution of the *nth* amplitude image is smaller than 0.1% of average image brightness, similar to the approach of (Dantas & Costa, 2007). Fig. 3(c) displays the MW output. A total of twenty simulated images are used in speckle filter evaluation. Fig. 4 displays typical results of filter application to the

The output of the local statistics filters vary in the speckle suppression level: the Lee, Frost and enhanced Frost remove most of the speckle pattern with some blurring. The Kuan and

II simulation software (Jensen, 1996) and demodulated to baseband.

Speckle free MW image.

pattern produced can be seen in Fig. 3(b).

simulated images.

where both images are of size *X* × *Y*. This metric is shown to have a significant inverse relationship with the Speckle Level expert score at the 1% significance level.

**Edge Region MSE** This is the same as the MSE above, but only pixels in the vicinity of image edges are considered.

This metric is shown to have a significant relationship with the Detail Clarity expert score at the 1% significance level.


Table 1. Intra-expert association between scoring categories and metrics, using Spearmans correlation (*ρ*), with significance.

Having established relationships between objective image quality metrics and subjective expert opinion, the present author recently conducted a comprehensive review of speckle filtering methods as applied to echocardiography (Finn et al., 2010). A comprehensive evaluation of a wide range of techniques was performed, taking into account both clinical and simulated ultrasound images, and also the computational requirements of each method. Fifteen recent filtering approaches, including anisotropic diffusion, wavelet denoising and local statistics, were evaluated. These are summarised in Table 2.


Table 2. Despeckle Filter Summary. *AD* = Anisotropic Diffusion, *W* = Wavelet.

16 Will-be-set-by-IN-TECH

where both images are of size *X* × *Y*. This metric is shown to have a significant inverse

**Edge Region MSE** This is the same as the MSE above, but only pixels in the vicinity of image

This metric is shown to have a significant relationship with the Detail Clarity expert score at

Overall Quality/ *ρ*=0.74 *ρ*=0.59 *ρ*=0.53 *ρ*=0.72 *ρ*=0.55 *ρ*=0.82 FOM p=176.5×10−<sup>11</sup> p=123.0×10−<sup>7</sup> p=124.1×10−<sup>6</sup> p=607.0×10−<sup>11</sup> p=452.7×10−<sup>7</sup> p=992.7×10−<sup>15</sup> Detail Clarity/ *ρ*=-0.67 *ρ*=-0.62 *ρ*=-0.49 *ρ*=-0.76 *ρ*=-0.49 *ρ*=-0.83 Edge Region MSE p=164.0×10−<sup>9</sup> p=240.0×10−<sup>8</sup> p=402.0×10−<sup>6</sup> p=346.8×10−<sup>12</sup> p=332.9×10−<sup>6</sup> p=205.6×10−<sup>15</sup> Speckle Level/ *ρ*=-0.69 *ρ*=-0.47 *ρ*=-0.85 *ρ*=-0.47 *ρ*=-0.64 *ρ*=-0.87 MSE p=531.1×10−<sup>10</sup> p=726.0×10−<sup>6</sup> p=306.8×10−<sup>16</sup> p=710.1×10−<sup>6</sup> p=992.1×10−<sup>9</sup> p=214.3×10−<sup>17</sup>

Table 1. Intra-expert association between scoring categories and metrics, using Spearmans

local statistics, were evaluated. These are summarised in Table 2.

Having established relationships between objective image quality metrics and subjective expert opinion, the present author recently conducted a comprehensive review of speckle filtering methods as applied to echocardiography (Finn et al., 2010). A comprehensive evaluation of a wide range of techniques was performed, taking into account both clinical and simulated ultrasound images, and also the computational requirements of each method. Fifteen recent filtering approaches, including anisotropic diffusion, wavelet denoising and

**Method Type Refrences Abbreviation** Perona and Malik Diffusion AD Perona & Malik (1990) PMAD

(2006) DPAD

Diffusion AD Yu & Acton (2002) SRAD

Diffusion AD Weickert (1999) CED Nonlinear Coherent Diffusion AD Abd-Elmoniem et al. (2002) NCD

Anisotropic Diffusion AD Krissian et al. (2007) OSRAD Zong *et al.* Filter W Zong et al. (1998) Zong

Method <sup>W</sup> Pižurica et al. (2003) GLM

Diffusion <sup>W</sup> Yue et al. (2006) NMWD Lee Filter SAR Lee (1980) Lee Frost *et al.* Filter SAR Frost et al. (1982) Frost Kuan *et al.* Filter SAR Kuan et al. (1987) Kuan Enhanced Lee Filter SAR Lopes et al. (1990) EnhLee Enhanced Frost *et al.* Filter SAR Lopes et al. (1990) EnhFrost Geometric Filter - Crimmins (1985) Geo

Diffusion AD Aja-Fernandez & Alberola-Lopez

Table 2. Despeckle Filter Summary. *AD* = Anisotropic Diffusion, *W* = Wavelet.

**Expert 1 Expert 2 Expert 3 Expert 4 Expert 5 Expert 6**

relationship with the Speckle Level expert score at the 1% significance level.

edges are considered.

the 1% significance level.

correlation (*ρ*), with significance.

Speckle Reducing Anisotropic

Detail Preserving Anisotropic

Coherence Enhancing

Oriented Speckle Reducing

Generalized Likelihood

Nonlinear Multiscale Wavelet

Fig. 3. Example simulated ultrasound image. (a) Echomap, (b) Speckled amplitude image, (c) Speckle free MW image.

Various approaches of varying simplicity have been employed in the literature to produce simulated images (Achim et al., 2001; Sattar et al., 1997; Yu & Acton, 2002). Ultrasound imaging can be treated as a linear process (Jensen, 1991; Ng et al., 2006), i.e. the filtering of an echogenicity map with a point spread function (PSF). An axially-varying PSF was used in (Ng et al., 2007), approximated as piecewise constant, similar to (Michailovich & Adam, 2005). This approach was also employed here, with PSFs at various depths generated using the Field II simulation software (Jensen, 1996) and demodulated to baseband.

While the PSF models the imaging system, the imaged medium is modelled as an echogenicity map *h*(*x*, *y*) composed of complex point scatterers, similar to (Dantas & Costa, 2007). Scatterers are positioned randomly within regions of varying density. The phase values of the scatterers follows a uniform distribution, varying from 0 → 2*π* rad, while scatterer magnitude follows a Gaussian distribution with unity mean and *σ* = 0.1. Fig. 3(a) shows an example of an echomap with two regions of differing scatterer densities, with density values of 40% and 10%. Echogenicity maps are filtered to generate a simulated image as *RF*(*x*, *y*) = *h*(*x*, *y*) ∗ *p*(*x*, *y*), *I*(*x*, *y*) = |*RF*(*x*, *y*)|. where *p* is the analytic form of the PSF function at the correct depth, and ∗ denotes convolution. Examples of the granular speckle pattern produced can be seen in Fig. 3(b).

The Maximum Writing (MW) technique (Burckhardt, 1978) is used to generate a maximally speckle free version of each of the twenty simulated images. The above convolution is performed multiple times, randomly varying scatterer phase. This produces a series of images with the same structure but differing speckle patterns, the maximum of which is the speckle free image: *IMW* <sup>=</sup> max{|*p*(*x*, *<sup>y</sup>*) <sup>∗</sup> (|*h*(*x*, *<sup>y</sup>*)<sup>|</sup> exp[*φn*])|} (*φ<sup>n</sup>* is the phase of the *<sup>n</sup>th* set of scatterers generated). In practice, this technique is applied until the contribution of the *nth* amplitude image is smaller than 0.1% of average image brightness, similar to the approach of (Dantas & Costa, 2007). Fig. 3(c) displays the MW output. A total of twenty simulated images are used in speckle filter evaluation. Fig. 4 displays typical results of filter application to the simulated images.

The output of the local statistics filters vary in the speckle suppression level: the Lee, Frost and enhanced Frost remove most of the speckle pattern with some blurring. The Kuan and

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Speckle Reduction in Echocardiography: Trends and Perceptions 59

ehhanced Lee filter remove considerably less of the speckle pattern. The anisotropic diffusion filters also exhibit a range of output quality. The PMAD filter required many iterations to remove speckle, resulting in a blurred output. The SRAD and DPAD filters both display strong speckle suppression. Due to a larger window size, the DPAD filter remove more of the speckle, producing images which are more uniform. The CED method and the NCD filter both display artefacts, introduced by the enhancement of image contours (including those of the speckle texture). This effect is more pronounced for the NCD filter. The OSRAD filter displays a strong degree of speckle suppression, and preserves the image borders. The Zong and GLM filter outputs both show a degree of speckle remaining. The NMWD filter is seen to produce output with most of the speckle pattern removed. Finally, the Geometric filters output displays a good level of speckle reduction, however some of the speckle pattern does still remain.

A set of clinical images are used in evaluation. A total of 500 frames are used to evaluate filtering performance, taken from 100 videos from 40 patients. They were scanned using a General Electric Vivid 7 Series scanner (GE Healthcare, Piscataway, NJ, USA). The results of

The local statistics filters output are quite similar in appearance, and still contain some speckle. As with the simulated images, the anisotropic diffusion filters produce output with a range of characteristics. The PMAD filter produces images which are extremely blurred. The SRAD and DPAD filters both show strong speckle suppression, however the SRAD output appears more distorted. As with the simulated images, the CED and NCD filters introduce small scale artefacts to the images. The OSRAD filter again shows strong speckle suppression. Frames processed with the Zong wavelet filter have a somewhat washed-out appearance, and not all of the speckle is removed. The GLM, NMWD and Geometric filtered frames have most of the

Five image quality metrics are applied to both the simulated and clinical echocardiographic images. In addition to the FoM and the edge MSE are detailed above, the following are

**Structural Similarity (SSIM)** The SSIM measure (Wang et al., 2004) to asses the preservation

where *μ*1, *μ*<sup>2</sup> and *σ*1, *σ*<sup>2</sup> are the means and standard deviations of the images being compared, and *σ*<sup>12</sup> is the covariance between them. These quantities are calculated using local statistics within a total of *M* windows, the average of which is taken in (26). Constants *C*1, *C*<sup>2</sup> � 1 ensure stability (Wang et al., 2004), and *M* is chosen as 32. The SSIM has values in the 0 → 1

**Contrast to Noise Ratio (CNR)** The CNR quantifies the level of contrast between a region of

*CNR* <sup>=</sup> <sup>|</sup>*μ*<sup>1</sup> <sup>−</sup> *<sup>μ</sup>*2<sup>|</sup> *σ*2 <sup>1</sup> <sup>+</sup> *<sup>σ</sup>*<sup>2</sup> 2

(*μ*<sup>2</sup> <sup>1</sup> <sup>+</sup> *<sup>μ</sup>*<sup>2</sup>

*<sup>M</sup>* <sup>∑</sup> (2*μ*1*μ*<sup>2</sup> <sup>+</sup> *<sup>C</sup>*1)(2*σ*<sup>12</sup> <sup>+</sup> *<sup>C</sup>*2)

<sup>2</sup> <sup>+</sup> *<sup>C</sup>*1)(*σ*<sup>2</sup>

<sup>1</sup> <sup>+</sup> *<sup>σ</sup>*<sup>2</sup>

<sup>2</sup> <sup>+</sup> *<sup>C</sup>*2) (26)

(27)

applying the filters to the image of Fig. 1(a) are shown in Fig. 5.

speckle removed, however the GLM output appears slightly blurred.

of structural information in the filtering process:

*SSIM* <sup>=</sup> <sup>1</sup>

range, with unity representing structurally identical images.

interest and the background, and is calculated as:

considered:

Fig. 4. Sample speckle filter output for a simulated image. (a) Lee, (b) Kuan, (c) Frost, (d) EnhLee, (e) EnhFrost, (f) PMAD, (g) SRAD, (h) DPAD, (i) CED, (j) NCD, (k) OSRAD, (l) Zong, (m) GLM, (n) NMWD, (o) Geo.

ehhanced Lee filter remove considerably less of the speckle pattern. The anisotropic diffusion filters also exhibit a range of output quality. The PMAD filter required many iterations to remove speckle, resulting in a blurred output. The SRAD and DPAD filters both display strong speckle suppression. Due to a larger window size, the DPAD filter remove more of the speckle, producing images which are more uniform. The CED method and the NCD filter both display artefacts, introduced by the enhancement of image contours (including those of the speckle texture). This effect is more pronounced for the NCD filter. The OSRAD filter displays a strong degree of speckle suppression, and preserves the image borders. The Zong and GLM filter outputs both show a degree of speckle remaining. The NMWD filter is seen to produce output with most of the speckle pattern removed. Finally, the Geometric filters output displays a good level of speckle reduction, however some of the speckle pattern does still remain.

A set of clinical images are used in evaluation. A total of 500 frames are used to evaluate filtering performance, taken from 100 videos from 40 patients. They were scanned using a General Electric Vivid 7 Series scanner (GE Healthcare, Piscataway, NJ, USA). The results of applying the filters to the image of Fig. 1(a) are shown in Fig. 5.

The local statistics filters output are quite similar in appearance, and still contain some speckle. As with the simulated images, the anisotropic diffusion filters produce output with a range of characteristics. The PMAD filter produces images which are extremely blurred. The SRAD and DPAD filters both show strong speckle suppression, however the SRAD output appears more distorted. As with the simulated images, the CED and NCD filters introduce small scale artefacts to the images. The OSRAD filter again shows strong speckle suppression. Frames processed with the Zong wavelet filter have a somewhat washed-out appearance, and not all of the speckle is removed. The GLM, NMWD and Geometric filtered frames have most of the speckle removed, however the GLM output appears slightly blurred.

Five image quality metrics are applied to both the simulated and clinical echocardiographic images. In addition to the FoM and the edge MSE are detailed above, the following are considered:

**Structural Similarity (SSIM)** The SSIM measure (Wang et al., 2004) to asses the preservation of structural information in the filtering process:

$$SSIM = \frac{1}{M} \sum \frac{(2\mu\_1\mu\_2 + \mathcal{C}\_1)(2\sigma\_{12} + \mathcal{C}\_2)}{(\mu\_1^2 + \mu\_2^2 + \mathcal{C}\_1)(\sigma\_1^2 + \sigma\_2^2 + \mathcal{C}\_2)}\tag{26}$$

where *μ*1, *μ*<sup>2</sup> and *σ*1, *σ*<sup>2</sup> are the means and standard deviations of the images being compared, and *σ*<sup>12</sup> is the covariance between them. These quantities are calculated using local statistics within a total of *M* windows, the average of which is taken in (26). Constants *C*1, *C*<sup>2</sup> � 1 ensure stability (Wang et al., 2004), and *M* is chosen as 32. The SSIM has values in the 0 → 1 range, with unity representing structurally identical images.

**Contrast to Noise Ratio (CNR)** The CNR quantifies the level of contrast between a region of interest and the background, and is calculated as:

Fig. 4. Sample speckle filter output for a simulated image. (a) Lee, (b) Kuan, (c) Frost, (d) EnhLee, (e) EnhFrost, (f) PMAD, (g) SRAD, (h) DPAD, (i) CED, (j) NCD, (k) OSRAD, (l) Zong,

(m) (n) (o)

18 Will-be-set-by-IN-TECH

(a) (b) (c) (d)

(e) (f) (g) (h)

(i) (j) (k) (l)

(m) GLM, (n) NMWD, (o) Geo.

$$\text{CNR} = \frac{|\mu\_1 - \mu\_2|}{\sqrt{\sigma\_1^2 + \sigma\_2^2}} \tag{27}$$

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Speckle Reduction in Echocardiography: Trends and Perceptions 61

reduction. The OSRAD filter exceeds the average *SNRA* of the MW reference in one image region, and matches it in another. SRAD exceeds the MW reference average *SNRA* in a single image region. The rest of the anisotropic diffusion methods have varying results as quantified by *SNRA*. The NCD, DPAD and PMAD filters are rated highly, however the CED method performs poorly. Of the SAR filters, the Lee filter achieves the highest *SNRA* score. Apart

Application of the other image quality metrics to the simulated images shows that the OSRAD, CED and NCD filters have the lowest edge region MSE, i.e. the smallest difference in the intensity of pixels close to image edges. By contrast, the FoM metric quantifies the average distortion in edge pixel locations between each filtered image and the MW reference image. The filters which perform best here are the Zong wavelet filter and the SAR filters. The filters with output most similar to the MW edges, as measured by the edge region MSE, perform poorly in the FoM. The SSIM metric compares the average structural similarity of filtered output with the MW reference. Calculated values are quite low, with the CED filter having the highest average of 0.22. Thus the speckle filters output are not structurally similar to the MW reference images. The CNR metric quantifies the average difference in contrast between each filtered output and the corresponding MW reference. Negative CNR values here indicate a lower contrast value than the MW reference. Over one third of the filters show improved average contrast relative to the MW image, the greatest of which are for the PMAD and

Applying metrics to the output of the clinical image set shows that the filters which remove the most speckle are the same as in the simulated case, although the level of improvement in the *SNRA* metric is lower than for the simulated images. The smaller *SNRA* increase can be explained by the differences in image content between the simulated and clinical images. Unlike the simulated images, the clinical images contain specular as well as scattered reflections. In addition they contain deviations from Rayleigh statistics (Molthen et al., 1995). The OSRAD filter achieves the highest average FoM value. The diffusion filters in general achieve mixed FoM scores, while some of the SAR filters achieve quite high scores. The Enhanced Lee, Frost and Zong filters are on average the most similar to the speckled input according to the SSIM metric. For the Enhanced Lee and Frost filters, the *SNRA* values indicate that this may be due to a low level of overall filtering. The CNR shows that the contrast increases for all post processing filters, with the OSRAD, SRAD and NMWD attaining the greatest improvement. The lowest average difference in edge region pixel intensity due to filtering is observed for the NMWD and OSRAD filters. The Frost, CED and Kuan filters also

preserve the content of edge region pixels quite well as measured by this metric.

The computational requirements for each of the filtering methods are determined by calculation of the number of multiplications, additions, and look-up table operations. A number of considerations are detailed here. For the anisotropic diffusion filters, the choice of discretization method has a large impact on computational requirements. A discretization scheme which allows the choice of a larger timestep (*τ*) can achieve a given level of diffusion with less iterations. Three discretization methods were compared: a simple explicit scheme, the Additive Operator Splitting (AOS) scheme of (Weickert et al., 1998), and the Jacobi scheme of (Krissian et al., 2007). For each of these methods the error is found relative to a reference diffusion (explicit discretization with a very small *τ*) for the diffusion methods of (Perona & Malik, 1990) and (Aja-Fernandez & Alberola-Lopez, 2006). The error for all

from the NMWD filter, the wavelet based methods perform quite poorly in this test.

OSRAD filters.

Fig. 5. Speckle filter output for the clinical image of Fig. 1(a). (a) Lee, (b) Kuan, (c) Frost, (d) EnhLee, (e) EnhFrost, (f) PMAD, (g) SRAD, (h) DPAD, (i) CED, (j) NCD, (k) OSRAD, (l) Zong, (m) GLM, (n) NMWD, (o) Geo.

where *μ*<sup>1</sup> and *σ*<sup>2</sup> <sup>1</sup> are the mean and variance of a region of interest, and *<sup>μ</sup>*<sup>2</sup> and *<sup>σ</sup>*<sup>2</sup> <sup>2</sup> are the mean and variance of a similar sized region in the image background.

**SNRA** Burckhardt's (Burckhardt, 1978) *SNRA* quantifies the level of speckle as the ratio of mean to standard deviation of the amplitude values.

For the simulated images, the *SNRA* metric shows that the level of speckle is reduced by all of the filters. The MW reference has a higher average *SNRA* than the post processing filters as expected, although some post processing filters exceed or match the MW *SNRA* in individual regions. The NMWD and OSRAD filters achieve the highest average *SNRA* values of the speckle reduction filters. The SRAD filter also performs well in this measure of speckle 20 Will-be-set-by-IN-TECH

(a) (b) (c) (d)

(e) (f) (g) (h)

(i) (j) (k) (l)

(m) (n) (o)

Fig. 5. Speckle filter output for the clinical image of Fig. 1(a). (a) Lee, (b) Kuan, (c) Frost, (d) EnhLee, (e) EnhFrost, (f) PMAD, (g) SRAD, (h) DPAD, (i) CED, (j) NCD, (k) OSRAD, (l) Zong,

<sup>1</sup> are the mean and variance of a region of interest, and *<sup>μ</sup>*<sup>2</sup> and *<sup>σ</sup>*<sup>2</sup>

**SNRA** Burckhardt's (Burckhardt, 1978) *SNRA* quantifies the level of speckle as the ratio of

For the simulated images, the *SNRA* metric shows that the level of speckle is reduced by all of the filters. The MW reference has a higher average *SNRA* than the post processing filters as expected, although some post processing filters exceed or match the MW *SNRA* in individual regions. The NMWD and OSRAD filters achieve the highest average *SNRA* values of the speckle reduction filters. The SRAD filter also performs well in this measure of speckle

and variance of a similar sized region in the image background.

mean to standard deviation of the amplitude values.

<sup>2</sup> are the mean

(m) GLM, (n) NMWD, (o) Geo.

where *μ*<sup>1</sup> and *σ*<sup>2</sup>

reduction. The OSRAD filter exceeds the average *SNRA* of the MW reference in one image region, and matches it in another. SRAD exceeds the MW reference average *SNRA* in a single image region. The rest of the anisotropic diffusion methods have varying results as quantified by *SNRA*. The NCD, DPAD and PMAD filters are rated highly, however the CED method performs poorly. Of the SAR filters, the Lee filter achieves the highest *SNRA* score. Apart from the NMWD filter, the wavelet based methods perform quite poorly in this test.

Application of the other image quality metrics to the simulated images shows that the OSRAD, CED and NCD filters have the lowest edge region MSE, i.e. the smallest difference in the intensity of pixels close to image edges. By contrast, the FoM metric quantifies the average distortion in edge pixel locations between each filtered image and the MW reference image. The filters which perform best here are the Zong wavelet filter and the SAR filters. The filters with output most similar to the MW edges, as measured by the edge region MSE, perform poorly in the FoM. The SSIM metric compares the average structural similarity of filtered output with the MW reference. Calculated values are quite low, with the CED filter having the highest average of 0.22. Thus the speckle filters output are not structurally similar to the MW reference images. The CNR metric quantifies the average difference in contrast between each filtered output and the corresponding MW reference. Negative CNR values here indicate a lower contrast value than the MW reference. Over one third of the filters show improved average contrast relative to the MW image, the greatest of which are for the PMAD and OSRAD filters.

Applying metrics to the output of the clinical image set shows that the filters which remove the most speckle are the same as in the simulated case, although the level of improvement in the *SNRA* metric is lower than for the simulated images. The smaller *SNRA* increase can be explained by the differences in image content between the simulated and clinical images. Unlike the simulated images, the clinical images contain specular as well as scattered reflections. In addition they contain deviations from Rayleigh statistics (Molthen et al., 1995). The OSRAD filter achieves the highest average FoM value. The diffusion filters in general achieve mixed FoM scores, while some of the SAR filters achieve quite high scores. The Enhanced Lee, Frost and Zong filters are on average the most similar to the speckled input according to the SSIM metric. For the Enhanced Lee and Frost filters, the *SNRA* values indicate that this may be due to a low level of overall filtering. The CNR shows that the contrast increases for all post processing filters, with the OSRAD, SRAD and NMWD attaining the greatest improvement. The lowest average difference in edge region pixel intensity due to filtering is observed for the NMWD and OSRAD filters. The Frost, CED and Kuan filters also preserve the content of edge region pixels quite well as measured by this metric.

The computational requirements for each of the filtering methods are determined by calculation of the number of multiplications, additions, and look-up table operations. A number of considerations are detailed here. For the anisotropic diffusion filters, the choice of discretization method has a large impact on computational requirements. A discretization scheme which allows the choice of a larger timestep (*τ*) can achieve a given level of diffusion with less iterations. Three discretization methods were compared: a simple explicit scheme, the Additive Operator Splitting (AOS) scheme of (Weickert et al., 1998), and the Jacobi scheme of (Krissian et al., 2007). For each of these methods the error is found relative to a reference diffusion (explicit discretization with a very small *τ*) for the diffusion methods of (Perona & Malik, 1990) and (Aja-Fernandez & Alberola-Lopez, 2006). The error for all

Trends and Perceptions 23

Speckle Reduction in Echocardiography: Trends and Perceptions 63

using this approach is very close to that of the NMWD, with the advantage of a much smaller processing overhead. The OSRAD method was therefore considered the best compromise.

This chapter has presented an overview of the speckle artefact from ultrasound, with a focus on echocardiography. A description of nature and modelling of speckle was presented. The reduction or removal of speckle from clinical ultrasound and echocardiography is a common goal of image processing in the literature, and many of the recent approaches are detailed in

The assessment of the quality of speckle reduced video is not a straightforward task. In the literature, many methods of review focus on numerical metrics and visual analysis without consideration of clinical opinion. For the case of clinical echocardiography, the extension of assessment technique to include expert physician opinion allows a more realistic evaluation. Image quality metrics are still of high importance however, due to their ease of computation

This chapter has described a study in which the relationships between such metrics and objective expert opinion are explored, and it was found that certain metrics are strong indicators of physicians assessment. An extensive study of a large number of speckle reduction filters is also described above, focusing on real world application. A large number of speckled images, both clinical and simulated, are used as test data. Assessment includes image quality metrics (some of which are indicators of physicians evaluation) and also a

An important aspect of evaluating the quality of speckle reduced echocardiography is that there are often differences between clinical and image processing perspectives. In particular, clinical experts do not appear to prefer the use of speckle filtered images for diagnostic analysis. It should be noted that there are situations where speckle preservation is desired. In particular, clinicians may prefer the original speckled images in some situations (Zhang et al., 2007). Dantas and Costa (Dantas & Costa, 2007) noted that when speckle is removed, the loss of false fine detail can lead to a perceived reduction in image sharpness, even if the boundaries of anatomical structures are not blurred. The speckle pattern is seen as having diagnostic utility in specific conditions, such as diffuse liver diseases (Kadah et al., 1996) in abdominal imaging and hypertrophic cardiomyopathy in echocardiography (Massay et al., 1989). Some automated processing tasks take advantage of the speckle pattern, such as feature tracking (Trahey et al., 1987) and tissue characterisation, some recent examples of which can be found in (De Marchi et al., 2006; Maurice et al., 2005; Tsui et al., 2005). So while some particular applications are best served by preserving speckle, others benefit from its removal. Perhaps the most pragmatic approach was taken by Zhang *et al.* (Zhang et al., 2007), who promote the idea of the speckle reduced image as a complementary addition to the original image, rather

Abd-Elmoniem, K., Youssef, A.-B. & Kadah, Y. (2002). Real-time speckle reduction and

coherence enhancement in ultrasound imaging via nonlinear anisotropic diffusion,

**5. Conclusion**

Section 3 above.

and their objective nature.

than a replacement.

**6. References**

computational requirement analysis.

discretisation schemes increases with larger *τ*. The error measured for the explicit scheme is small as expected, but the valid range of *τ* is constrained to small values. The error for the AOS scheme and the Jacobi method are higher than the explicit method. It is observed that the AOS scheme performs similarly for both the PMAD and DPAD diffusion methods, while the Jacobi discretization results in a significantly higher error for one of the diffusion functions. Further details can be found in (Finn et al., 2010). In the analysis of computational requirements, various other implementational details are considered, which are also detailed in this paper.

After quantification of the filter complexity for each filter, it was found that the most computationally intensive method is the NMWD filter, for typical filtering scenarios. This filter required almost five times as many multiplications as the next most demanding. The DPAD and SRAD filters have higher requirements than the other diffusion methods, but this is due to the large number of iterations required. The DWT used in the GLM filter requires much more computation than the DWT of the Zong filter. The efficiency of the semi-implicit scheme for the anisotropic diffusion filters is demonstrated by the similarity between their requirements and the SAR filters.

The use of simulated images permits comparison of speckle reduced filtered output with a maximally noise free reference. Quantification of speckle reduction capabilities using the *SNRA* has shown that anisotropic diffusion based methods have in general the strongest suppression of speckle. The application of objective metrics such as the FoM, Edge MSE, CNR and SSIM quantifies other aspects of the filtering process. The improvement in CNR values of the SRAD, OSRAD and NMWD filters shows that these methods can achieve greater contrast than other methods.. Average edge pixel distortion due to filtering was lowest in the matrix diffusion and SAR filters, as seen by both the high FoM and low edge region MSE values. This indicates that these methods distort image boundaries the least amount. In the case of the SAR filters however, this is due to a low overall level of filtering.

Based on analysis of computational complexity, it is clear that there is a large disparity in the requirements of the speckle reduction methods considered here. The SAR and geometric filters have the lowest computational overhead, but this comes at the expense of lower speckle reduction capability. The wavelet based approaches are hindered from a performance perspective by the requirements of implementing wavelet analysis and reconstruction. In particular, the NMWD filter performs wavelet analysis and reconstruction for each iteration, leading to the largest requirement of all considered methods. The anisotropic diffusion methods all have similar processing needs, and these fall between those of the SAR methods and the wavelet based filters. Efficient implementation of these methods is only possible by the use of a discretisation method which allows a large timestep.

This study concluded by noting that the optimal filtering method for echocardiography depends on the scenario: If the main concern is a constraint on available processing capability, the SAR filters are the best due to their low requirements. In particular the Lee filter is a reasonable choice given its speckle suppression ability and low overhead. If however the main objective is to remove as much speckle as possible, the NMWD filter has the strongest speckle suppression capabilities. This comes at the expense of the highest computational complexity however, and the preservation of edges is not optimal. The OSRAD method represents the best trade-off between both of these situations. The level of speckle suppression achievable

using this approach is very close to that of the NMWD, with the advantage of a much smaller processing overhead. The OSRAD method was therefore considered the best compromise.

#### **5. Conclusion**

22 Will-be-set-by-IN-TECH

discretisation schemes increases with larger *τ*. The error measured for the explicit scheme is small as expected, but the valid range of *τ* is constrained to small values. The error for the AOS scheme and the Jacobi method are higher than the explicit method. It is observed that the AOS scheme performs similarly for both the PMAD and DPAD diffusion methods, while the Jacobi discretization results in a significantly higher error for one of the diffusion functions. Further details can be found in (Finn et al., 2010). In the analysis of computational requirements, various other implementational details are considered, which are also detailed

After quantification of the filter complexity for each filter, it was found that the most computationally intensive method is the NMWD filter, for typical filtering scenarios. This filter required almost five times as many multiplications as the next most demanding. The DPAD and SRAD filters have higher requirements than the other diffusion methods, but this is due to the large number of iterations required. The DWT used in the GLM filter requires much more computation than the DWT of the Zong filter. The efficiency of the semi-implicit scheme for the anisotropic diffusion filters is demonstrated by the similarity between their

The use of simulated images permits comparison of speckle reduced filtered output with a maximally noise free reference. Quantification of speckle reduction capabilities using the *SNRA* has shown that anisotropic diffusion based methods have in general the strongest suppression of speckle. The application of objective metrics such as the FoM, Edge MSE, CNR and SSIM quantifies other aspects of the filtering process. The improvement in CNR values of the SRAD, OSRAD and NMWD filters shows that these methods can achieve greater contrast than other methods.. Average edge pixel distortion due to filtering was lowest in the matrix diffusion and SAR filters, as seen by both the high FoM and low edge region MSE values. This indicates that these methods distort image boundaries the least amount. In the case of

Based on analysis of computational complexity, it is clear that there is a large disparity in the requirements of the speckle reduction methods considered here. The SAR and geometric filters have the lowest computational overhead, but this comes at the expense of lower speckle reduction capability. The wavelet based approaches are hindered from a performance perspective by the requirements of implementing wavelet analysis and reconstruction. In particular, the NMWD filter performs wavelet analysis and reconstruction for each iteration, leading to the largest requirement of all considered methods. The anisotropic diffusion methods all have similar processing needs, and these fall between those of the SAR methods and the wavelet based filters. Efficient implementation of these methods is only possible by

This study concluded by noting that the optimal filtering method for echocardiography depends on the scenario: If the main concern is a constraint on available processing capability, the SAR filters are the best due to their low requirements. In particular the Lee filter is a reasonable choice given its speckle suppression ability and low overhead. If however the main objective is to remove as much speckle as possible, the NMWD filter has the strongest speckle suppression capabilities. This comes at the expense of the highest computational complexity however, and the preservation of edges is not optimal. The OSRAD method represents the best trade-off between both of these situations. The level of speckle suppression achievable

the SAR filters however, this is due to a low overall level of filtering.

the use of a discretisation method which allows a large timestep.

in this paper.

requirements and the SAR filters.

This chapter has presented an overview of the speckle artefact from ultrasound, with a focus on echocardiography. A description of nature and modelling of speckle was presented. The reduction or removal of speckle from clinical ultrasound and echocardiography is a common goal of image processing in the literature, and many of the recent approaches are detailed in Section 3 above.

The assessment of the quality of speckle reduced video is not a straightforward task. In the literature, many methods of review focus on numerical metrics and visual analysis without consideration of clinical opinion. For the case of clinical echocardiography, the extension of assessment technique to include expert physician opinion allows a more realistic evaluation. Image quality metrics are still of high importance however, due to their ease of computation and their objective nature.

This chapter has described a study in which the relationships between such metrics and objective expert opinion are explored, and it was found that certain metrics are strong indicators of physicians assessment. An extensive study of a large number of speckle reduction filters is also described above, focusing on real world application. A large number of speckled images, both clinical and simulated, are used as test data. Assessment includes image quality metrics (some of which are indicators of physicians evaluation) and also a computational requirement analysis.

An important aspect of evaluating the quality of speckle reduced echocardiography is that there are often differences between clinical and image processing perspectives. In particular, clinical experts do not appear to prefer the use of speckle filtered images for diagnostic analysis. It should be noted that there are situations where speckle preservation is desired. In particular, clinicians may prefer the original speckled images in some situations (Zhang et al., 2007). Dantas and Costa (Dantas & Costa, 2007) noted that when speckle is removed, the loss of false fine detail can lead to a perceived reduction in image sharpness, even if the boundaries of anatomical structures are not blurred. The speckle pattern is seen as having diagnostic utility in specific conditions, such as diffuse liver diseases (Kadah et al., 1996) in abdominal imaging and hypertrophic cardiomyopathy in echocardiography (Massay et al., 1989). Some automated processing tasks take advantage of the speckle pattern, such as feature tracking (Trahey et al., 1987) and tissue characterisation, some recent examples of which can be found in (De Marchi et al., 2006; Maurice et al., 2005; Tsui et al., 2005). So while some particular applications are best served by preserving speckle, others benefit from its removal. Perhaps the most pragmatic approach was taken by Zhang *et al.* (Zhang et al., 2007), who promote the idea of the speckle reduced image as a complementary addition to the original image, rather than a replacement.

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**4** 

*USA* 

**Speckle Detection in Echocardiographic Images** 

B-scan Echocardiographic images unlikely carry unlikely images by scattering of ultrasound beams backed from structures within the body organ that is being scanned. Two major types of scatterings are diffused and coherent scatterings. Diffuse scatterings are caused when there are a large number of scatterers is with random phase within the resolution cell of the ultrasound beam and causes speckles in the reconstructed image; whereas the e coherent scattering arises when the scatterers in the resolution cell are in phase and causes light or dark spots in the image. Rayleigh distribution is the most common statistical model for the envelope signal and assumes that a large number of scatterers per resolution cell exist. However in some ultrasonic imaging fields such as echocardiography, Rayleigh distribution fits to reflect properties of reflections from blood but fails with complex structures such as myocardial tissue. The K distribution , on the other hand, was initially designed for the envelope signal and have been proposed to model different kinds of tissue in ultrasound envelope imaging. This distribution also has the advantage to model both fully and partially developed speckle. The first-order envelope statistics have been thought to follow a Rayleigh distribution, but recent work has shown that more general models, such as the

Nakagami, K, and homodyned K distributions better describe envelope statistics.

unsupervised clustering techniques in this study.

With the current digital ultrasound imaging, the radio-frequency (RF) signal has gained more interest as it may contain more information than the envelope echo. When there are a large number of scatterers per range cell it yields Gaussian statistics for the RF signal, but the statistics of the RF signal in the case of partially developed speckle don't follow the Gaussian distribution. Therefore, in this study to model statistical behaviour of the RF data, we used K distribution framework, described in and for such statistics applied them to the RF data. By splitting the ultrasound image to image patches, statistical features for image patches can be extracted using the statistical modelling of the RF signal. These features could overlap for some tissues and the pattern classification approaches should be utilized to classify tissues based on the extracted statistical features. Over past decades, several supervised and unsupervised classification and segmentation algorithms have been proposed to process the medical images. Some of these techniques are listed in. Because of above mentioned problems (overlap between statistical features of tissues) and the fact that in our application (speckle classification), we cannot have enough training material and the data size (=number of image patches) is finite and small, we only focused on the

**1. Introduction** 

Arezou Akbarian Azar, Hasan Rivaz and Emad M. Boctor *The Russell H. Morgan Department of Radiology and Radiological Science* 

*The Johns Hopkins University School of Medicine, Baltimore* 

