**2. Common speckle filters**

Speckle reducing filters are originated from the synthetic aperture radar community [10]. Later these filters are applied to ultrasound imaging since the early 1980s [11]. There are two major classifications of speckle reduction filters, viz. single scale spatial filters and transform domain multiscale filters. The spatial filter acts on an image by smoothing it; that is, it reduces the intensity variation between adjacent pixels. The simple sliding window spatial filter replaces the center value in the window with the average of all the neighboring pixel values including itself. By doing this, it replaces pixels, that are unrepresentative of their surroundings. It is implemented with a convolution mask, which provides a result that is a weighted sum of the values of a pixel and its neighbors. It is also called a linear filter. The mask or kernel is a square. Often a 3× 3 square kernel is used. If the coefficients of the mask sum up to one, then the average brightness of the image is not changed. If the coefficients sum to zero, the average brightness is lost, and it returns a dark image.

The common speckle filters such as Lee, Kuan and Wiener filters are considered for the study. The brief definition and mathematical description of the standard spatial filters are discussed below:

#### *Lee filter:*

( ) ( )

åå å - (7)

ij ij ij ij 2 2 2 2 2 2 ij ij ij ij

where the summations are done over both the indices i and j from 0 to N-1. If the correlation coefficient is near to +1, then there exists stronger positive correlation between the original

*Computational time*: The computational time (Tc) of a filter is defined as the time taken by a digital computing platform to execute the filtering algorithm when no other software, except the operating system, runs on it. Normally, Tc depends on the computing system's clock time period. But, in addition to the clock period, it depends on the memory size, the input data size, and the memory access time, etc. The computational time taken by a filter should be low for online and real time image processing applications. Hence, a filter with lower Tc is better than a filter having higher Tc value while all other performance measures remain identical.

For the purpose of experimentation, a medical ultrasound image database is prepared in consultation with a medical expert for the present study. The images are acquired using the instrument GE LOGIQ 3 Expert system with 5 MHz transducer frequency, in JPEG format.

In the present Chapter, the aim of the study is to address, novel issues related to despeckling medical ultrasound images. It is envisaged that the results of this investigation would be used as a pre processing step for effective image segmentation or image registration techniques in

The remaining part of this Chapter is organised into five sections. The section 2 deals with common speckle filters. The section 3 examines wavelet transform methods, while the section 4 investigates contourlet transform methods. The section 5 describes the Gaussian model of

Speckle reducing filters are originated from the synthetic aperture radar community [10]. Later these filters are applied to ultrasound imaging since the early 1980s [11]. There are two major classifications of speckle reduction filters, viz. single scale spatial filters and transform domain multiscale filters. The spatial filter acts on an image by smoothing it; that is, it reduces the intensity variation between adjacent pixels. The simple sliding window spatial filter replaces the center value in the window with the average of all the neighboring pixel values including itself. By doing this, it replaces pixels, that are unrepresentative of their surroundings. It is implemented with a convolution mask, which provides a result that is a weighted sum of the values of a pixel and its neighbors. It is also called a linear filter. The mask or kernel is a square.

The data set consists of 70 ultrasound images of size 512x512, of kidney and liver.

speckle noise. Finally, the section 6 gives the conclusions.

N XY X Y

N X- X N Y Y å åå -

2

CC

image and despeckled image.

204 Advancements and Breakthroughs in Ultrasound Imaging

**1.2. Image data set**

other applications also.

**2. Common speckle filters**

=

The Lee filter [12] is based on the approach that the smoothing is performed on the area having low variance. However, smoothing will not be performed on area of high variance, which is near edges. The Lee filter assumes that the image can be approximated by a linear model represented by Eq.(8)

$$\mathbf{Y}\_{\mathrm{ij}} = \overline{\mathbf{K}} + \mathbf{W}^\* \mathbf{(C} - \overline{\mathbf{K}}) \tag{8}$$

where Yij is the gray scale value of the pixel at ( i, j) after filtering. If there is no smoothing, the filter will output, only the mean intensity value K¯ of the kernel K, otherwise, the difference between the centre pixel C and K¯ is calculated and multiplied with a weighting function W given in Eq.(9) :

$$\mathbf{W} = \frac{\sigma\_k^2}{\{\sigma\_k^2 \star \sigma^2\}} \tag{9}$$

and then summed with K¯, where <sup>σ</sup><sup>k</sup> <sup>2</sup> is the variance of the pixel values within the kernel given by the Eq. (10):

$$
\sigma\_{\mathbf{k}}^2 = \frac{1}{M^2} \sum\_{\mathbf{u}, \mathbf{v} = 0}^{M \cdot 1} \left( \mathbf{K}\_{\mathbf{u} \mathbf{v}} \cdot \overline{\mathbf{K}} \right)^2 \tag{10}
$$

where MxM is the size of the kernel and Kuv is the pixel value within the kernel at indices u and v, K¯ is the mean intensity value of kernel. The parameter <sup>σ</sup><sup>2</sup> is the variance of the image X, which is given by the Eq.(3). The main disadvantage of Lee filter is that it tends to ignore speckle noise in the areas closest to edges and lines.

#### *Kuan filter:*

The Kuan filter [13] is a generalization of the Lee filter. The Kuan filter converts the multipli‐ cative model of speckle into an additive linear form. However, it is based on the equivalent number of looks (ENL), which is computed from an ultrasound image to determine a different weighting function W given by the Eq.(11):

$$\mathbf{W} = \frac{\left(\mathbf{1} \cdot \mathbf{C}\_u / \mathbf{C}\_i\right)}{\left(\mathbf{1} \cdot \mathbf{C}\_u\right)}.\tag{11}$$

The weighting function is computed from estimated noise variation coefficient of the image, Cu given by the Eq.(12):

$$\mathbf{C}\_{u} = \text{(ENL)}^{\frac{1}{T}} \tag{12}$$

and the variation coefficient Ci of the image given by the Eq. (13):

$$\mathbf{C}\_{\mathbf{i}} = \sigma\_{\mathbf{k}} / \bar{\mathbf{K}} \tag{13}$$

where ENL is given by the Eq.(14) :

$$\text{ENLL} = \left(\frac{\overline{\mathbf{K}}}{\sigma\_{\mathbf{k}}}\right)^2 \tag{14}$$

depending upon the local variance and thus tries to hold the true original value as far as

Filters

PSNR SNR

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207

Speckle Noise Reduction in Medical Ultrasound Images

The Lee filter and Wiener filter are implemented using kernel size 3x3, 5x5, 7x7 and Kuan filter using kernel size 3x3 and 5x5.The classical Wiener filter, is not adequate for removing speckle, since it is designed mainly for additive noise suppression. To address the multiplicative nature of speckle noise, a homomorphic approach is developed in [15], which converts the multipli‐ cative noise into additive noise, by taking the logarithm of image and then applies the Wiener filter. The PSNR, SNR, CC, variance and MSE are considered as filter performance measures. The Figures 1.-4. show the average results obtained for 70 ultrasound images, which are despeckled using Kuan, Lee and Wiener filter. The optimality is determined by the criteria, namely (i) higher SNR and PSNR values, (ii) lower variance, MSE values and (iii) Correlation Coefficient is nearly equal to one. From the Figures 1.-4., it is observed that Wiener filter with kernel size 3x3 gives better results than other despeckling filters. The computational time of different filters are given in the Table 1. The filter having less computational time is usually required for online and real time applications. The least value of computation is highlighted. From the Table 1, it is observed that Wiener filter with kernel size 3x3 is better among all the

For proper judgement of performance of filters, the subjective evaluation should be taken into consideration. For subjective evaluation, the despeckled images of various filters are shown in the Figure 5. From the Figure 5, it is observed from visual inspection that all the three methods achieved good speckle suppression performance. However, Lee and Kuan filters lost many of the signal details and the resulting images are blurred. Further, Wiener filter with kernel size 3x3 yielded better visual enhancement of medical ultrasound images. However, the Lee filter smoothes away noise in flat regions, but leaves the fine details such as lines and

Thus the main disadvantage of Lee filter is that, it tends to ignore speckle noise in the area closest to edges and lines. The Kuan filter is considered to be more superior to the Lee filter. It does not make an approximation on the noise variance within the filter window. The only

filters compared here, for despeckling medical ultrasound images.

**Figure 1.** Performance of various despeckling filters, in terms of PSNR, SNR.

possible.

PSNR,SNR

 (indB)

texture unchanged.

In the Eq.(14), the σ<sup>k</sup> is the standard deviation of the kernel and K¯ is the mean intensity value of the kernel. The only disadvantage of the Kuan filter is that the ENL parameter needs to be computed.

#### *Wiener filter:*

The Wiener filter [14] is a linear spatial domain filter. There are two alternatives : (i) Fourier transform method ( frequency domain) (ii) mean squared method (spatial domain), for implementing the Wiener filter. The first alternative is used for denoising and deblurring, whereas the second alternative is used for denoising only. The frequency domain alternative of Wiener filtering requires a prior knowledge of noise power spectra and the original image. But, in the spatial domain alternative, no such prior knowledge is required. It is based on statistical least squared principle and minimizes the mean squared error between actual signal sequence and desired signal sequence.

In an image, the statistical properties differ too much from one region to another region. Thus, both global statistics (mean, variance, and higher order moments of entire image) and local statistics (mean, variance, and higher order moments of kernel) are important. Wiener filtering is based on both, global and local statistics and is given by

$$\mathbf{Y}\_{\mathrm{ij}} = \overline{\mathbf{K}} + \frac{\sigma\_{\mathbf{k}}^2}{\sigma\_{\mathbf{k}}^2 + \sigma^2} \left( \mathbf{K}\_{\mathrm{uv}} \cdot \overline{\mathbf{K}} \right) \tag{15}$$

where Yij denotes the despeckled image, K¯ is the local mean, σ<sup>k</sup> <sup>2</sup> is the local variance, Kuv is (u, v)th pixel in the kernel K and σ<sup>2</sup> is the global variance. Let us consider kernel of size MxM, then local variance σ<sup>k</sup> 2 is defined by Eq.(10). From the Eq.(15), it is observed that the filter output is equal to local mean if the centre pixel value equals local mean, or else it outputs the modified value different from local mean. Thus, filter output varies from the local mean

 **Figure 1.** Performance of various despeckling filters, in terms of PSNR, SNR.

The weighting function is computed from estimated noise variation coefficient of the image,


of the image given by the Eq. (13):

2

In the Eq.(14), the σ<sup>k</sup> is the standard deviation of the kernel and K¯ is the mean intensity value of the kernel. The only disadvantage of the Kuan filter is that the ENL parameter needs to be

The Wiener filter [14] is a linear spatial domain filter. There are two alternatives : (i) Fourier transform method ( frequency domain) (ii) mean squared method (spatial domain), for implementing the Wiener filter. The first alternative is used for denoising and deblurring, whereas the second alternative is used for denoising only. The frequency domain alternative of Wiener filtering requires a prior knowledge of noise power spectra and the original image. But, in the spatial domain alternative, no such prior knowledge is required. It is based on statistical least squared principle and minimizes the mean squared error between actual signal

In an image, the statistical properties differ too much from one region to another region. Thus, both global statistics (mean, variance, and higher order moments of entire image) and local statistics (mean, variance, and higher order moments of kernel) are important. Wiener filtering

(u, v)th pixel in the kernel K and σ<sup>2</sup> is the global variance. Let us consider kernel of size MxM,

output is equal to local mean if the centre pixel value equals local mean, or else it outputs the modified value different from local mean. Thus, filter output varies from the local mean

2 is defined by Eq.(10). From the Eq.(15), it is observed that the filter

<sup>2</sup> (12)

(14)

Ci=σ<sup>k</sup> / K¯ (13)

<sup>2</sup> <sup>+</sup> <sup>σ</sup><sup>2</sup> (Kuv - K¯) (15)

<sup>2</sup> is the local variance, Kuv is

Cu =(ENL)

<sup>K</sup> ENL <sup>σ</sup><sup>k</sup> æ ö ç ÷ <sup>=</sup> ç ÷ è ø

Cu given by the Eq.(12):

computed. *Wiener filter:*

and the variation coefficient Ci

206 Advancements and Breakthroughs in Ultrasound Imaging

where ENL is given by the Eq.(14) :

sequence and desired signal sequence.

then local variance σ<sup>k</sup>

is based on both, global and local statistics and is given by

Yij

where Yij denotes the despeckled image, K¯ is the local mean, σ<sup>k</sup>

=K¯ <sup>+</sup> <sup>σ</sup><sup>k</sup> 2 σk

depending upon the local variance and thus tries to hold the true original value as far as possible.

The Lee filter and Wiener filter are implemented using kernel size 3x3, 5x5, 7x7 and Kuan filter using kernel size 3x3 and 5x5.The classical Wiener filter, is not adequate for removing speckle, since it is designed mainly for additive noise suppression. To address the multiplicative nature of speckle noise, a homomorphic approach is developed in [15], which converts the multipli‐ cative noise into additive noise, by taking the logarithm of image and then applies the Wiener filter. The PSNR, SNR, CC, variance and MSE are considered as filter performance measures. The Figures 1.-4. show the average results obtained for 70 ultrasound images, which are despeckled using Kuan, Lee and Wiener filter. The optimality is determined by the criteria, namely (i) higher SNR and PSNR values, (ii) lower variance, MSE values and (iii) Correlation Coefficient is nearly equal to one. From the Figures 1.-4., it is observed that Wiener filter with kernel size 3x3 gives better results than other despeckling filters. The computational time of different filters are given in the Table 1. The filter having less computational time is usually required for online and real time applications. The least value of computation is highlighted. From the Table 1, it is observed that Wiener filter with kernel size 3x3 is better among all the filters compared here, for despeckling medical ultrasound images.

For proper judgement of performance of filters, the subjective evaluation should be taken into consideration. For subjective evaluation, the despeckled images of various filters are shown in the Figure 5. From the Figure 5, it is observed from visual inspection that all the three methods achieved good speckle suppression performance. However, Lee and Kuan filters lost many of the signal details and the resulting images are blurred. Further, Wiener filter with kernel size 3x3 yielded better visual enhancement of medical ultrasound images. However, the Lee filter smoothes away noise in flat regions, but leaves the fine details such as lines and texture unchanged.

Thus the main disadvantage of Lee filter is that, it tends to ignore speckle noise in the area closest to edges and lines. The Kuan filter is considered to be more superior to the Lee filter. It does not make an approximation on the noise variance within the filter window. The only

**Figure 2.** Performance of various despeckling filters, in terms of variance

**Figure 3.** Performance of various despeckling filters, in terms of MSE.

enhancement of medical ultrasound images. Further, for the complete removal of speckle without losing any data is not possible at the moment. This is because all of these filters rely on local statistical data related to the filtered pixel. An alternative approach is to use wavelet

**Figure 5.** Performance comparison of various despeckling filters by visual inspection of an ultrasound image of kidney.

(g)Wiener(3x3) (h)Wiener(5x5) (i)Wiener(7x7)

(a)Original image (b)Kuan(3x3) (c)Kuan(5x5)

Speckle Noise Reduction in Medical Ultrasound Images

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209

(d)Lee(5x5) (e)Lee(7x7) (f)Lee (3x3)

The primary goal of speckle reduction is to remove the speckle without losing much detail contained in an image. To achieve this goal, we make use of the wavelet transform and apply multiresolution analysis to localize an image into different frequency components or useful

transform.

**3. Wavelet transform method**

**Figure 4.** Performance of various despeckling filters, in terms of Correlation Coefficient

limitation of Kuan filter is the high computational time due to estimation of ENL parameter. The Wiener filter with kernel size 3×3 is effective in preserving the edges and other detailed information upto some extent. Further, when the various spatial domain filters are compared by visual inspection, it is observed that Wiener filter with kernel size 3×3 yielded better visual

**Figure 5.** Performance comparison of various despeckling filters by visual inspection of an ultrasound image of kidney.

enhancement of medical ultrasound images. Further, for the complete removal of speckle without losing any data is not possible at the moment. This is because all of these filters rely on local statistical data related to the filtered pixel. An alternative approach is to use wavelet transform.
