Image Denoising

#### **Chapter 3**

## SAR Image Denoising Using MMSE Techniques

*Mohamed Yahia and Tarig Ali*

#### **Abstract**

Synthetic aperture radar (SAR) provides many advantages over optical remote sensing, principally the all-weather and all-day acquisition capability. For this reason, SAR images have been exploited for many applications such as forestry, agriculture, disaster monitoring, sea/ice monitoring. However, the main limitation in SAR images is the contamination with the multiplicative speckle noise. The speckle damages the radiometric quality of SAR images and contracts the performance of information extraction techniques. Many methods have been proposed in the literature to reduce speckle noise. These methods, however, must avoid degrading the useful information in the SAR images, such as textures, local mean of backscatter, and point targets. The minimum mean square error (MMSE) techniques have been largely applied in SAR image speckle denoising. The objective of this chapter is to review and give new insights into the MMSE denoising of SAR images. In particular, the performances of three MMSE-based techniques which are the commonly applied Lee sigma filter and the newly introduced iterative MMSE (IMMSE) filter, and the infinite number of looks prediction (INLP) filter are studied.

**Keywords:** SAR image denoising, MMSE techniques, Lee sigma filter, IMMSE filter, INLP filter

#### **1. Introduction**

Remote sensing imagery constitutes nowadays an important source of information for the characterization of the Earth's surface. The potentiality of synthetic aperture radar (SAR) systems is recognized for geoscience and remote sensing applications due to their operation in all-time and all-weather conditions. However, due to the coherent nature of the scattering mechanisms, SAR data are affected by the multiplicative speckle noise. The presence of speckle noise disturbs human interpretation of the images and reduces the accuracy of postprocessing such as image classification [1].

The multi-looking process (i.e., boxcar filter) reduces speckles by averaging the intensities of neighboring pixels [2]. Nevertheless, the spatial resolution is degraded. Many other denoising techniques have been introduced in the literature to alleviate this limitation by using other estimation domains including spatial [3] and wavelet [4]. In the intensity-driven adaptive-neighborhood (IDAN) filter a region-growing

technique is applied to produce an adaptive neighborhood [5]. The total variation (TV) techniques [6] have been widely applied for SAR image denoising due to their efficiency to preserve spatial details and speckle reduction. The nonlocal NL filtering represents one of the powerful speckle reduction techniques. Zhong et al. [7] applied the NL Means (NLM) to filter SAR images by adapting the use of Euclidean distance to multiplicative noise. The probabilistic patch based (PPB) filter introduces a patchbased weight to generalize the Euclidean distance-based weight used in the NL means algorithm [8]. A hybrid NL-wavelet domain denoising technique has been proposed [9]. Penna et al. replaced the Euclidean distance in the NLM filter with stochastic distances in the Haar wavelet domain [10]. The NL-based filters improved significantly the denoising performance of SAR images. However, their main disadvantage resides in the high computing cost. Deep Learning techniques constitute a recent trend of PolSAR speckle filtering [11–13].

The minimum mean square error (MMSE) based filters that account for the local statistics of the image constitute an important branch of speckle filtering techniques. Since the introduction of the Lee sigma filter in early 1980 [14, 15], many versions have been elaborated such as Frost [16], Kuan [17], the improved Lee [18, 19], etc. Due to their effectiveness in speckle reduction, simplicity and low computational demand, many MMSE-based filters have been implemented in remote sensing software. To mitigate the drawbacks of the Lee sigma filter, various versions of the iterative MMSE (IMMSE) filter have been introduced recently [20–26]. Based on the MMSE principle, it has been demonstrated that the filtered pixels and their variances are linearly related. Then, a linear regression of means and variances for different window sizes is applied to estimate the infinite number of looks prediction (INLP) filtered pixels [27–30]. In this chapter, the improved MMSE-based Lee sigma, the IMMSE, and the INLP denoising techniques are studied.

This paper is organized as follows: Section 2 reviews the classical MMSE-based denoising technique and presents the updated versions, i.e., INLP and IMMSE techniques. The results are shown in Section 3. Finally, Section 4 presents the conclusions of this paper.

#### **2. MMSE-based filters: classical version**

The intensity pixel *y(i)* of a SAR image is affected by a multiplicative noise [2]

$$
\varphi(i) = \mathfrak{x}(i)\,\,\nu(i),\tag{1}
$$

*x*(*i*) is the noise-free pixel and *ν*(*i*) is the speckle noise with unit mean and standard deviation *σν*. It is assumed that *x*(*i*) and *ν*(*i*) are statistically independent. In the rest of the chapter, the index (*i*) will be omitted. Let *x*^ and *x* be the estimated and the *a priori* mean of *x*, respectively.

From (1) we have

$$E(\mathfrak{y}) = E(\mathfrak{x}|\mathfrak{\nu}) = E(\mathfrak{x})\,\mathrm{E}(\mathfrak{\nu}) = E(\mathfrak{x})\tag{2}$$

where *E()* is a mathematical expectation (i.e., statistical mean). By exploiting the ergodicity of the SAR data, the statistical mean is substituted by the spatial mean, i.e.,

$$
\overline{\mathbf{y}} = \mathbf{E}(\mathbf{y}) = \mathbf{E}(\mathbf{x}) = \overline{\mathbf{x}} \tag{3}
$$

*SAR Image Denoising Using MMSE Techniques DOI: http://dx.doi.org/10.5772/intechopen.108362*

Nevertheless, it has been demonstrated recently that the statistical and spatial averaging statistics are quite different [27] since in the spatial averaging process the processing windows are overlapping, and a spatial correlation is introduced. Hence, replacing the statistical mean with the spatial one should be taken with caution.

The MMSE filter is assumed to be a linear combination of *x* and *x* [1]

$$
\hat{\mathfrak{x}} = a\overline{\mathfrak{x}} + by\tag{4}
$$

The parameters *a* and *b* are selected optimally to minimize the MSE

$$I = E\left[\left(\mathbf{x} \cdot \hat{\mathbf{x}}\right)^2\right] \tag{5}$$

then

$$\frac{\partial I}{\partial a} = \mathbf{0} \tag{6}$$

and

$$\frac{\partial I}{\partial b} = \mathbf{0} \tag{7}$$

This minimization leads to [1]

$$a = 1 - b \tag{8}$$

and

$$b = \frac{\text{var}(\mathbf{x})}{\text{var}(\mathbf{y})} \tag{9}$$

#### For a given X and Y two independent random variables, we have

$$\text{var.}(\mathbf{XY}) = \mathbf{E}(\mathbf{Y})^2 \text{var}(\mathbf{X}) + \text{var.}(\mathbf{Y})\text{var.}(\mathbf{X}) + \text{var.}(\mathbf{Y})\mathbf{E}(\mathbf{X})^2 \tag{10}$$

Then

$$\text{var}(\mathbf{y}) = \text{var}(\mathbf{x}|\nu) = \overline{\mathbf{x}}^2 \sigma\_v^2 + \text{var}(\mathbf{x}) \,\sigma\_v^2 + \overline{v}^2 \text{var}(\mathbf{x}) \tag{11}$$

Eq. (2) gives

$$
\overline{y} = \overline{x} \tag{12}
$$

then

$$\text{var}(\mathbf{x}) = \frac{\text{var}(\mathbf{y}) - \overline{\mathbf{y}}^2 \sigma\_\nu^2}{\mathbf{1} + \sigma\_\nu^2} \tag{13}$$

finally

$$
\hat{x} = \overline{y} + b(y - \overline{y}) \tag{14}
$$

$$b = \frac{\text{var}(y) - \overline{y}^2 \sigma\_\nu^2}{\text{var}(y) \left(1 + \sigma\_\nu^2\right)} \tag{15}$$

var(y) and *y* are estimated using a moving window W. *σ*<sup>2</sup> *<sup>ν</sup>* is assumed to be a constant (i.e., *σ*<sup>2</sup> *<sup>ν</sup>* ¼ 1 for single look SAR data).

#### **2.1 Lee sigma filter**

The Lee sigma filter has been implemented in several geographic information system (GIS) software due to its effectiveness in speckle reduction, its simplicity, and its computational efficiency. However, in amplitude and intensity SAR data, the probability density functions (pdf) are not symmetrical, because they follow the Rayleigh and the negative exponential distributions, respectively. This asymmetry produces biased estimates since the original sigma range was derived based on Gaussian distribution. Hence, to remove the bias and to preserve the mean value, the sigma ranges were recomputed based on the corresponding pdf. The sigma ranges of amplitude and intensity SAR data are given in [18]. In [28], the performance of the improved Lee sigma filter is revised.

*Practical implementation*


#### **3. MMSE-based filters: New insights**

#### **3.1 The IMMSE filter**

The objective of SAR speckle filtering is:


Hence in general cases, we have.

$$
\hat{\mathfrak{x}} \in [\mathfrak{y}, \overline{\mathfrak{y}}] \text{ or } \hat{\mathfrak{x}} \in [\overline{\mathfrak{y}}, \mathfrak{y}] \tag{16}
$$

The principle of the IMMSE filter is to scan the range of *x*^ in ½ � *y*, *y* by the following iterative procedure.

*SAR Image Denoising Using MMSE Techniques DOI: http://dx.doi.org/10.5772/intechopen.108362*

$$
\hat{\mathfrak{x}}\_0 = \overline{\mathfrak{y}},
\tag{17}
$$

$$
\hat{\mathfrak{x}}\_{k+1} = \hat{\mathfrak{x}}\_k + b'\_k(\mathfrak{y} \cdot \hat{\mathfrak{x}}\_k). \tag{18}
$$

If 0 <*b*<sup>0</sup> *<sup>k</sup>* < 1, then *x*^<sup>∞</sup> ¼ *y* and *x*^*<sup>k</sup>* ∈½ � *y*, *y* . The performance of the IMMSE denoising technique is the function of:


$$\text{i. } 0 \le b'\_{\text{k}} \le 1.$$

ii. *b*<sup>0</sup> *<sup>k</sup>*≈0 in homogeneous areas,

iii. *b*<sup>0</sup> *<sup>k</sup>*≈1 in heterogeneous areas.

Hence, by implementing *N* iterations (*N* is sufficiently low), the denoising procedure maintained the filtered homogeneous areas (i. e.*x*^*N*≈*x*^<sup>0</sup> since *b*<sup>0</sup> *k*≈0) and preserved spatial details (i. e.*x*^*<sup>N</sup>* ¼ *y* since *b*<sup>0</sup> *<sup>k</sup>*≈1).

By the analogy of the MMSE expression of the parameter *b* (15), the parameter *b'* has been expressed as

$$b\_k' = \frac{\text{var}(\hat{\mathbf{x}}\_k)}{\left(\left(\mathbf{1} + \sigma\_\nu^2\right)\text{var}(\hat{\mathbf{x}}\_k) + \hat{\mathbf{x}}\_k^{-2}\sigma\_\nu^2\right)}\tag{19}$$

In [21], the authors proposed a more sophisticated version expressed as

$$b'\_k = \tanh\left(\frac{\mathbf{C} \mathbf{V}^2\_{\hat{\mathbf{x}}\_k} \mathbf{C} \mathbf{V}^2\_{\mathbf{y}}}{\mathbf{C}}\right) \tag{20}$$

$$\mathbf{C} = \frac{\mathbf{1}}{\left(\text{ENL}\_0\right)^2},\tag{21}$$

where *CV* is the coefficient variation and *ENL*<sup>0</sup> is the equivalent number of looks of the original image *y* estimated in a homogenous area,

$$\text{CV}(\mathbf{y}) = \frac{\text{std}(\mathbf{y})}{\overline{\mathbf{y}}} \tag{22}$$

$$\text{ENL}\_0 = \frac{\left(\overline{y}\right)^2}{\text{var}(y)}\tag{23}$$

where *std* is the standard deviation.

#### **3.2 Practical implementation**

For a given SAR image *y*


Repeat iii to vii *K* iterations. *K* is a tuning parameter to control the speckle reduction and spatial detail preservation.

#### **3.3 The INLP filter**

The INLP is based on the statistics of the SAR intensity (i.e., multiplicative noise model (1) and the MMSE expression (14). In [26, 29–32], it has been demonstrated that.

$$
\hat{\mathfrak{x}} = a \mathbf{var}(\hat{\mathfrak{x}}) + d \tag{24}
$$

where

$$\mathfrak{a} = (\mathfrak{y} - \mathfrak{x}) / \text{var}(\mathfrak{x}),\tag{25}$$

and

$$d = \mathfrak{x}.\tag{26}$$

Eq. (24) shows that the filtered pixel *x*^ is linearly related to its variance varð Þ *x*^ . This rule is applied to estimate the INLP-filtered pixel (i.e., the parameter *d* or the noisefree pixel *x*). In the extended homogeneous area, the MMSE filtered pixel is *x*^ ¼ *x*≈*x* while in the INLP filter *x*^ ¼ *d*≈*x* where *d* is estimated using a linear regression between means and their variances and not using a simple mean (i.e., *x*^ ¼ *x*≈*x*) as in the original MMSE denoising technique.

#### **3.4 Practical implementation**

For each pixel of the image:

i. Define a window W having *N* samples.


#### **4. Results**

EPD-ROATo assesses the performance of the studied denoising techniques, airborne and spaceborne SAR images were used (see **Figure 1a**). For the spaceborne SAR

**Figure 1.** *(a) Original spaceborne SAR image, (b) Boxcar filter, (c) MMSE filter (i. e. improved sigma filter [18], (d) IMMSE filter [21].*

data, the Sentinel 1 C-band *vv* SAR image of Dubai UAE is considered. The airborne SAR is the *hh* image of Les-Landes site, France acquired by NASA JPL AIRSAR sensor (see **Figure 2a**)).

#### **4.1 Evaluation criteria**

In addition to visual inspections, quantitative parameters have been employed to assess the performance of the studied denoising techniques. The ENL was employed to evaluate speckle reduction level

$$ENL(i) = \frac{\left(\overline{\hat{\mathbf{x}}}(i)\right)^2}{\mathbf{var}(\hat{\mathbf{x}}(i))}.\tag{27}$$

The edge preservation degree based on the ratio of averages (EPD-ROA) [33] is used to assess the preservation of spatial details. The EPD-ROA in horizontal direction is:

$$EPD-ROA\_H(i) = \frac{\sum\_{m,n} |\hat{\mathbf{x}}(m,n)/\hat{\mathbf{x}}(m, \ n+1)|}{\sum\_{m,n} |y(m,n)/y(m, \ n+1)|},\tag{28}$$

where m and n are the xy coordinates of the pixel in the selected zone, respectively. EPD-ROAV is calculated by replacing in (28) the indexes (m,n + 1) by (m + 1, n). In general cases, EPD-ROA < 1. High EPD-ROA means a high ability for spatial detail preservation.

#### **4.2 MMSE vs IMMSE**

**Figure 1** displays the filtered denoised spaceborne SAR images using the boxcar filter (i.e., mean filter), the MMSE (improved Lee filter), and the IMMSE filters. It can be observed that the boxcar filter reduced the speckle noise but blurred spatial details. The MMSE filter improved the filtering performance. The IMMSE maintained the high speckle reduction of the initial filter and enhanced considerably the spatial details such as lines (see rectangles) and points (see arrows). It can be seen that the IMMSE outperforms the MMSE-based filter in terms of speckle reduction and spatial detail preservation. Quantitative results in **Table 1** confirmed visual interpretations where the IMMSE filter maintained the high speckle reduction level of the initially applied filter and enhanced spatial details. Quantitative results show also that the MMSE filter outperformed the boxcar filter in terms of speckle reduction and spatial detail preservation. The IMMSE gave better filtering results than the MMSE filter in terms of speckle reduction (ENLIMMSE(1124) > ENLMMSE(410)) and spatial detail preservation (EPDIMMSE(0.98) > EPDMMSE(0.94)).

#### **4.3 MMSE vs INLP**

**Figure 2** displays the filtered airborne images using the studied filters. It can be observed visually that the MMSE filter outperformed the boxcar filter. The INLP reduced the blurring effects introduced by the MMSE filter. This can be easily seen in lines (see rectangles). Concerning the speckle reduction, it is observed that the INLP filter ensured better filtering performance. In fact, the homogeneous areas appear smoother than the

*SAR Image Denoising Using MMSE Techniques DOI: http://dx.doi.org/10.5772/intechopen.108362*

**Figure 2.**

*(a) Original airborne SAR image, (b) Boxcar filter, (c) MMSE filter (i. e. improved sigma filter [18], (d) INLP filter [31].*


**Table 1.**

*Performances of the filters using spaceborne data.*


**Table 2.**

*Performances of the filters using airborne data.*

ones ensured by the MMSE filter (see circles). These results are recorded quantitatively in **Table 2** from which it is observed that the INLP filter outperformed the MMSE filter in terms of speckle reduction (ENLINLP(10) > ENLMMSE(9)) and spatial detail preservation (EPDINLP(0.85) > ENLMMSE(0.84)).

#### **5. Conclusion**

In this chapter, the authors reviewed the use of the MMSE-based speckle denoising techniques in SAR images. It has been shown that the MMSE-based filters (i.e., the improved Lee sigma filter) ensured high speckle denoising performance. Based on the MMSE principle, two improved MMSE versions have been introduced recently in the literature, i.e., the IMMSE and the INLP filters. The results showed that when the IMMSE is initialized with an image ensuring high speckle reduction, it ensures better denoising performance than the classical MMSE-based filters in terms of speckle filtering and spatial detail preservation. In the INLP filter, unlike the MMSE-based filters which estimated the noise-free pixels using spatial means, linear regressions between the filtered pixels and their variances for different window sizes are applied. Results show that this new strategy increased the filtering performance. Future researches will focus on the extension of the IMMSE and the INLP on additive image denoising.

#### **Nomenclature**


#### *SAR Image Denoising Using MMSE Techniques DOI: http://dx.doi.org/10.5772/intechopen.108362*


### **Author details**

Mohamed Yahia<sup>1</sup> \* and Tarig Ali2

1 Laboratoire de recherche modélisation analyse et commande de systèmes- MACS, Ecole Nationale d'Ingénieurs de Gabes – ENIG, Université de Gabes, Gabes, Tunisia

2 GIS and Mapping Laboratory, American University of Sharjah, Sharjah, UAE

\*Address all correspondence to: mohamed\_yahia1@yahoo.fr

© 2022 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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#### **Chapter 4**

## ANNHRPAA Based Deep Learning Image Processing for Pneumonia Detection

*Avaragollada Puravarga Mathada Prasanna Kumar and S.M. Vijaya*

#### **Abstract**

Pneumonia is a syndrome that is cause by a bacterial disease in the lungs. This disease is diagnosed through a chest X-ray. For triumphant treatment early diagnosis is important. This disease can be diagnosed through X-ray imagery. Sometimes due to the unclear chest X-ray image, it can be confused with the other bacterial disease. Consequently, to guide clinicians requires computer-aided diagnosis system. In this, a amalgam reverse transmission algorithms introduced by which erudition of multilayer network achieved. The clamor investigation of the system is performed by using artificial neural network (ANN). Convolution neural network model vgg19 employed to create a user-friendly webpage for diagnosing this disease. Simulated artificial neural network hybrid reverse propagation adaptive algorithm used for deep learning image processing method in our training stage. The test results showed for the vgg19 network is at an accurateness of 0.91.

**Keywords:** pneumonia, transfer learning, vgg19, deep learning, webpage

#### **1. Introduction**

Mounting scientific advancement, it is potential to use tools based on unfathomable learning frameworks to discover pneumonia based on upper body X-ray imagery. The confront here would be to aid the conclusion process which allows for expedited treatment and better scientific outcome.

Pneumonia is a bacterial infection in one or both lungs which causes the inflammation of lung tissue. Over 7% of the residents which is 450 million inhabitants are affected by this disease worldwide and 4 million dies every year [1]. In India during, 2016—158,176 deaths were reported, and we continue to have the uppermost number of child deaths all over the globe. On earth pneumonia day the report was released that by 2030 over 11 million under-five children will be dead due to this transferable disease [2]. In the nineteenth century, the father of modern medicine for revolutionizing sir William Osler said pneumonia is "captain of the men of death".

The virus can easily pass from person to person which make it spread rapidly. One of the common symptoms of COVID-19 that can be easily identified is fever. Since the virus outbreak, thermal screening using infrared thermometers are used at public places to check the body temperature to identify the indicated infected among crowd. This prevention still lacking because it spends a lot of time to check the body temperature from every person and the most importance is the close contact of the infected might lead to spreading it to the person who do the screening process or from the one in charge of screening to the checked people.

Clinical examination such as chest X-ray, blood test, and other techniques are used by doctors to diagnose pneumonia in patients. In this chest X-ray is cheaper because of the technology development in bio-medical equipment. Sometimes even the clinicians fail to detect this disease by x-ray images due to the disturbance in images. Recent technology such as artificial intelligence can be useful to mitigate the disease. Especially for the image classification convolution neural network (CNNs) show great results. The main idea behind CNN is that it is an simulated model of the human brain's visual cortex. Based on the presence of pneumonia chest X-ray images are classified in convolution neural network.

#### **2. Literature survey**

The researchers [3] compared two CNN networks to diagnose pneumonia disease. To train the model they used to convey learning and fine-tuning. The consequences of the two networks are compared after the training phase. The accuracy of Xception and vgg19 are 0.82 and 0.87 respectively. And precision for Xception is 0.86 and 0.82 for the normal and pneumonia datasets. The precision for vgg16 is 0.83 and 0.91 respectively for the normal and pneumonia datasets. Here exception is more flourishing in detect pneumonia cases and vgg16 is better in detecting normal cases.

In [4] researchers tried the dissimilar technique for minimizing dimensionality. They used the JSRT dataset which has 247 X-ray images. BSE-JSRT dataset can be extracted after removing the bone shadow (dataset 02). Segmented JSRT (dataset 03) and we can have segmented BSE-JSRT (dataset 04). T-SNE technique is use to remove outlier (dataset 05). Here highest accuracy is obtained from dataset 05 which is 0.71 and the lowest accuracy is dataset 04 which is 0.56. From bone outline dataset 02 we get 0.65 accuracy.

In this paper [5], the authors used the ANN implement for detect lung diseases like pneumonia, TB. The pre- processing techniques are Lung segmentation taking out Image classification. Back-propagation and feed-forward networks are used for image classification. The dataset use from Sassoon sanatorium of 80 patients. They achieved an correctness of 0.92. The limitation is when the CXR position and size change there is no robustness. In this [6] researchers have used CNN techniques such as resnet-50 to diagnose thorax disease using chest X-ray. In pre-processing techniques, the global division take input and local branch is trained after discovering local lesion province. Here resnet-50 has average accuracy of 0.841. The AG-CNN raises the accurateness up to 0.868.

The researchers in [7, 8] created a cheXNet algorithm which as CNN of 121 layers to diagnose the pneumonia disease. They have down scaled the image to 224\*224 sizes. In addition to normalization base on standard deviation and mean. The accuracy of cheX Net is 0.435. The Artificial Neural Network model by Prasanna Kumar and Vijaya [2] as Hybrid Back Propagation Adaptive Algorithm (ANNHBPAA) for clatter abolition. Adaptive clatter termination using ANN has been implementing on image signal and intelligent method for real-time signal noise cancellation based on neural networks.

Here [1, 9] the author has taken the data from 3 different hospitals for pneumonia detection. For classification, they have used the cheXNet model. And for the model training PyTorch, 0.2.0 is used. Overall, they have obtained 0.815 accuracies. But CNN does not perform well on the external data.

There has been to a great extent follow a line of investigation by Prasanna Kumar and Vijaya [10, 11] on active noise control (ANC) systems and obtainable simulated results for trans image facsimile systems. The working principle of the anticipated intelligent adaptive filter base noise cancellation system is the prolongation of prior work.

#### **3. Proposed solutions**

Known revelation intensity, the quantity of X-rays impinge on the long-suffering different at different location on the patient's remains. Confrontation of X-rays pass from side to side the patient's composition. Some are wrapped up by the patient at the same time as others exceed all the way through and are captivated by the imaging detector—an additional statistically controlled process with its own inherent noise characteristics. One time the X-rays have conceded throughout the patient, picture "information" enclosed in the spatial allocation of the X-ray fluence.

The patient's composition has shaped variation in the X-ray concentration that imaging system uses to create image. Picture "signal" is the inherent arithmetic "noise" connected with the X-ray creation method.

In distinction, when a huge quantity of radiation use, the visibility of the arithmetical noise exist very low, perhaps even hardly noticeable. Although this can outcome in a visually agreeable image, an unnecessarily high revelation level was used, consequential in overexposure to the patient.

Up to this point converse noise coupled with the statistical nature of X-ray production and their succeeding amalgamation by the patient. These process are controlled by indispensable laws of nature and, for any given X-ray acquisition, they establish the fundamental limit on image quality.

Final displayed image comes to that original threshold on image quality distinguish the total of "extra" noise that the detector introduce hooked on the image. This is fundamentally the proportion of the gesture to noise in the final image to the "unique" signal to noise at hand in the occurrence X-ray fluence. Detector forever adds some quantity of noise into the image so the DQE is forever less than 1 shown in **Figure 1A–C**.

Disperse increases as soon as imaging thicker areas of the corpse—such as the upper body. Conventional method of plummeting scatter is collimation, anti-scatter grids, and/or utilize an air-gap.

In image processing system, noise deletion using adaptive digital sieve is a wellknown technique for extract most wanted images gesture by eliminate noise from the lossy picture contained indication tainted by noise. For noise annulment an assortment of gradient adaptive lattice (GAL) and LMS algorithms use. Of late, the cross adaptive algorithms with neural set of connections have gained popularity in cancelling the noise available in image compression and enhancement system. The operational principle of the planned intelligent adaptive filter-based noise cancellation system (AFNCS) is the extension of prior work Kumar et al. [12] which is additional empirically designed and computer-generated to enhance the performance of the input synthetic signal with high opinion to denoising.

#### **Figure 1.**

*A (left): Erect Portable Chest @ 105 kVp, 3.2 mAs with 6:1, 103 In/in Grid; B (center): Same patient, same SID @ 95 kVp, 2.8 mAs, no Grid, processed with Smart Grid; C (right): Same capture as B without Smart Grid.*

This intelligent hybrid reverse transmission algorithm involves both GAL and LMS algorithm. The prime objective of the proposed intelligent AFNCS is to acquire signal as of reference signal and output noisy signal, in the middle of this signal noise is eliminated by subtracting the reference signal and noisy signal with original signal. Significantly reinstate the original signal by eliminate the noise by means of adaptive control and adaptation of weights from beginning to end ANN. The following **Figure 2**, indicate the chunk depiction of the AFNCS which intakes the input signal "*i*(*t*)" and generate signal at output "*O*(*t*)" by means of adaptive system and orientation signal "*R*(*t*)". Lastly, the signal with errore(t) is computed by finding the difference amongst reference signal and output signal as given in (1).

$$e(t) = R(t) - O(t) \tag{1}$$

Every where '*t*' represent number of epochs.

Implementation of mixture algorithm consider this inaccuracy signal *e*(*t*) to produce a purpose for execution. This function perform the working out of required filter coefficients. The minimize error rate indicate that yield signal is similar as that of sole signal. Here reverse propagation algorithms are use to estimate the error speed of every neuron. The following **Figure 2** things to see the structural representation of

**Figure 2.** *Proposed adaptive filter based noise cancellation system (AFNCS).*

*ANNHRPAA Based Deep Learning Image Processing for Pneumonia Detection DOI: http://dx.doi.org/10.5772/intechopen.106640*

reverse propagation level diagram of ANN network. The layer diagram of ANN network is finished up of three layers comprising input layer, concealed layer and output layer. The hidden layer is active in among input and output layer which couple both the layers. Overall back propagation network is affected by one neuron error. The network allow image signal to propagate by means of ANN and provides output signal. As given in Eq. (1) the error results of the output layer are computed and this error is forward reverse to participation layer from beginning to end hidden layer in anticipation of the considered necessary output.

Added, to reduce its inaccuracy signal, fine-tuning of weight is to execute for every neurons. Projected hybrid algorithm combine both the reverse propagation algorithm of LMS and GAL which help to embark upon sluggish convergence.

The proposed AFNCS revealed in **Figure 1** adopt adaptive filter for carrying out of ANN in addition to as well adopt a control method for fine-tuning of adaptive filter parameter. The elements association is train with ANN by credence fine-tuning. The output of ANN can be obtained by using below formula as given in (2). The following **Table 1**, indicates the parameters used in design.

$$\text{ANN}\_{\text{out}} = \sum i(t) \times W\_{\text{g}} \tag{2}$$

Each of the input are accompany by a weight. If, P*Wg* ≥*Th*

Then the output of ANN will be 1 given in (3)

$$\text{ANN}\_{out} = \mathbf{1} \tag{3}$$

#### **3.1 Data**

In this study, a dataset consisting of 5842 chest X-ray images provided in **Table 1** by Guangzhou Women and Children's Medical Centre, Guangzhou. The X-ray images in the dataset are of different resolutions such as 1328 � 1160 and 1762 � 1535. The number of no pneumonia is 1576, and pneumonia is 4266. **Figure 3** shows some X-ray image samples from the dataset. In our models 0 represents normal cases, 1 represents pneumonia cases.


**Table 1.** *Distribution of dataset.*

**Figure 3.** *Data samples from the dataset.*

#### **3.2 Pre-processing**

In Deep learning, we need more data to be obtained for better and reliable results. However, there might not be more data or enough data for some problems, especially on medical problems. so, to avoid this, experts have some solutions to solve this problem. One of them is data augmentation which avoids over fitting and improves accuracy. It is supported in the Keras deep learning library image data generator class shown in **Figure 4**. Here we use rescale, shear range, Zoom range, Horizontal flip. We pre-process our X-ray images dataset before it is used for diagnosing pneumonia. The pre-processing has been performed as in following:

Unify X-ray images. Before inputting the images into our model, we downscale the images to 224 � 224 and convert them to a NumPy array. It can be suitable for features extraction by VGG. Perform image data argumentation methods, it is supported in the Keras deep learning library via the image data Generator class. Here we use rescale, shear range, Zoom range, Horizontal flip.

#### **3.3 Architecture**

AlexNet, AlexNetOWTBn, GoogleNet, VGG models are the most commonly used in transfer learning. They are a stack of many convolution layers. we have many difficulties with deep Convolution neural networks they are optimization of the network, desertion gradient problem, and deprivation problems. The VGG NET brings a new idea in place. It is used to solve complicated tasks and also increases detection accuracy. VggNet tries to resolve the difficulty in the training process of deep Convolution neural networks, the saturation, and degradation of correctness. In this paper, we have used Vgg19 architecture shown in **Figure 5**. Vgg19 network Vgg19 has 19 layers (16 convolution layers, 3 fully connected layers, 5 MaxPool layers, and 1 SoftMax layer).

#### **Figure 4.**

*(a) Rescale, (b) zoom range, (c) horizontal flip and (d) shear range for we use rescale, shear range, Zoom range, Horizontal flip. Pre-process our X-ray images dataset before it is used for diagnosing pneumonia.*

*ANNHRPAA Based Deep Learning Image Processing for Pneumonia Detection DOI: http://dx.doi.org/10.5772/intechopen.106640*

3 � 3 filters are used in the first and second layers in the convolutional layer. Here in the first and second layer totally 64 layers are used which results in 224 � 224 � 64 volume as the same convolution used. 3 � 3 filters are always used with a stride of 1. The next layer is the pooling layer, here to reduce the width and height volume from 224 � 224 � 64 to 112 � 112 � 64 we use the max pool of 2 � 2 size and stride of 2 Next it is followed by 2 convolution layers which as 128 filters. Therefore, it gives the new dimension of 112 � 112 � 128. Here pooling layer is used again to reduce the size to 56 � 56 � 128. Now 256 filters of 2 convolution layers are added then it is reduced to 28 � 28 � 256 by down sampling layer. Then the stack of 3 convolution layers is separated with 1 max-pooling layer. Finally, in the last pooling layer, we get 7 � 7 � 512 volume which is flattened into a fully connected layer with a total channel of 4096 and 1 classes of soft Max output.

#### **4. Hardware explanation**

In the projected method, the convergence speed of error signal increase with the value of St. LMS mechanism is adopt in the proposed method because of its easier

**Figure 6.** *Hardware experimental board.*

accomplishment, easy computational, dynamic usage of memory capability and is performed by adjusting filter coefficient for error reduction.

To estimate the performance of the projected adaptive noise cancellation algorithm by replication, the proposed algorithm is implemented on the experimental panel. As revealed in **Figure 6**, the experimental board includes one major board and one D to A/A to D data exchange card. The 16-bit D/A data exchange card is used to produce two signals. One signal is the communication signals.

Initially, the time impediment opinion performance and noise cancellation performance are evaluated in different mixed SNR environment, in that order. Secondly, the noise cancellation performance of proposed algorithm is evaluated when the time delay between the primary input and reference input is changing.

### **5. Experimental method**

In order to authenticate the feasibility of the projected algorithm adaptive noise cancellation system based is built on FPGA, which is revealed in **Figure 7**.

In a mathematical computing atmosphere projected model by means of soft computation-based algorithm design and implementation. The system stipulation required for performance includes a 64-bit operating system, an x64-based processor supported with 4.00 GB installed memory (RAM), where the processor type is Intel® Core™ i-8250U,CPU@1.80GHz

**Figure 7.** *Adaptive noise cancellation system.*

#### **5.1 Performed tests**

We have tried many testing in different experimental setups to analyze the performance of the proposed model. We have changed several network parameters and instructions to create the model. We have split the total dataset into 80% for training purposes and 20% for validation purposes. Then, we have experimented with the dataset with our proposed model.

#### **5.2 Fine-tuning**

Fine-enhancement is a method used to increase the effectiveness of a task. It make small changes to improve the outcome. Changing the parameters is so critical that several modify affect the training process a lot for the calculation time desirable the swiftness of convergence and the use of doling out units. Parameters setup for the proposed model given in **Table 2**. This process of fine-tuning was repeated again and again to improve the accuracy of our model.

#### **5.3 Training**

We have collected 5842 X-ray images in total as our database from Guangzhou Women and Children's Medical Centre, Guangzhou, where the number of no pneumonia is 1576, and pneumonia is 4266. All the images are graded into 2 classes (NORMAL & PNEUMONIA) by professional graders and used to train the model. And it is tested with 624 images.

To train the model, we have used the pretrained vggNet, which is initialized with weights trained on ImageNet which gave better results.

#### **5.4 Performance of the proposed model**

The model which we have created will start training with the training dataset which consists of both the actual images and the images from the augmentation Then we have used the validation dataset to generalize the model.

Furthermore, we can see the spreading of losses (both training loss and validation loss) concerning the number of epochs in both the training and validation phases

In this paper with the proposed model, the X-ray images were resized into 224 � 224. Then we have done the data augmentation. We used the weights of the pretrained vgg19 model. We have used Adam optimizer, and we have used the SoftMax


#### **Table 2.**

*Parameters setup for the proposed model.*

**Figure 8.** *Pretrained VGG-19 performance for pneumonia prediction task.*

#### **Figure 9.**

*Output of the model predicted with real data.*

activation function and batch size equals 32. In our model, we have set the learning rate, decay, momentum as default values.

Then we started training our vgg19 model, after training, we have got the accuracy score of the model which is 0.91 where we have used the standard ImageNet weights to train the model shown in **Figures 8** and **9**.

We have trained our model up to 20 epochs; the training was stopped owing to the absence of further improvement in both accuracy and loss.

Difference between actual and predicted is given in corresponding error Column for the 6 neuron layers obtained for 5000 iterations shown in **Table 3** and in **Figure 10** gives Comparison of LMS, GAL, hybrid correlation coefficient for 5000 and 10,000 iterations.

#### **6. Results**

To predict pneumonia disease, we have created a webpage using flask API. Once Flask API is designed. We can add the trained h5 file in the flask API then we can use



**Table 3.**

*Neurons hidden layer, 5000 iterations.*

#### **Figure 10.**

*Comparison of LMS, GAL, hybrid correlation coefficient for 5000 and 10,000 iterations.*

#### **Figure 11.**

*Webpage which predicts the disease when input is given.*

the flask run command in the command prompt to run the flask file and create a running webpage link which we can put in the browser to see the webpage.

**Figure 11** shows the pneumonia disease input screen. Where user can input their X-ray image by pressing the upload button, once the user clicks on the predict button it will return whether the patient has pneumonia disease or not **Figure 12** shows the output of the predicted results.


**Table 4.** *Performance attainment.*

#### **7. Bench mark**

In the base paper they have used vgg16 and Xception model for performing training. We have used extension of vgg which is vgg19, which as more trainable parameter and gives better accuracy than vgg16 which used in our base paper. In vgg16 we have 138 million parameter and in vgg19 we have 144 million parameters. Vgg19 is the deeper version vgg16 (**Table 4**).

#### **8. Conclusion**

Projected hybrid adaptive algorithms participation signals are deterministic. LMS as well as GAL algorithms are stochastic. Adaptive noise annulment using hybrid adaptive algorithms implement. Compare in the midst of conventional algorithms, the hybrid adaptive algorithms reveal that extremely fast convergence. Amid persistent enhancement of the adaptive hybrid algorithm in addition to the rapid development of signal processing chip it will be further widely use in mobile telecommunication system, in addition to signal processing fields. The simulation perception investigation of hybrid adaptive algorithms is conceded out on the convergence behaviour, correlation coefficient and convergence time. After comparing, simulated results were tabulated. By taking into consideration of accessible algorithms performance of hybrid adaptive algorithms gives enhanced convergence time, convergence behaviour, correlation coefficients. This technique is more systematic in eliminate noise from corrupted signal furthermore has less time to converge, faster response and reduction in memory.

Convolution Neural Network used to identify the pneumonia disease automatically. To train this model employed transfer learning method and carried out finetuning to improve the performance of the model, our model can distinguish between 2 classes of pneumonia or normal. The Vgg19 model which we have used has shown significant performance. Results obtained confirm attained valid accuracy up to 0.91 for classifying the pneumonia disease. Inference that our model has great practical significance in early pneumonia screening and diagnosis and has strong potential to be applied in other disease.

#### **Author details**

Avaragollada Puravarga Mathada Prasanna Kumar<sup>1</sup> \* and S.M. Vijaya<sup>2</sup>

1 Department of Electronics and Communication Engineering, ACS College of Engineering, Bengaluru, Karnataka, India

2 Department of Electronics and Communication Engineering, Rajarajeswari College of Engineering, Bengaluru, Karnataka, India

\*Address all correspondence to: amprasannakumar@acsce.edu.in

© 2022 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

*ANNHRPAA Based Deep Learning Image Processing for Pneumonia Detection DOI: http://dx.doi.org/10.5772/intechopen.106640*

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[2] Prasanna Kumar AM, Vijaya SM. ANNHBPAA based noise cancellation employing adaptive digital filters for mobile applications. Journal of the Institution of Engineers (India). 2021; **102**(4):645-653

[3] Ayan E, Murat H. Diagnosis of Pneumonia from Chest X-Ray Images Using Deep Learning. Kırıkkale, Turkey: Kırıkkale University, IEEE; 2019

[4] Gang P, Wang Z, Zeng W, Gordienko Y, Kochura Y, Alienin O, et al. Dimensionality reduction in deep learning for chest x-ray analysis of lung cancer. In: ICACI 2018: 10th International Conference on Advanced Computational Intelligence, Xiamen, China. IEEE; 2018. pp. 878-883

[5] Khobragade S, Tiwari A, Patil CY, Narke V. Automatic detection of major lung diseases using Chest Radiographs and classification by feed-forward artificial neural network. In: IEEE 1st International Conference on Power Electronics, Intelligent Control and Energy Systems. Delhi, India: Institute of Electrical and Electronics; 2016. pp. 1-5

[6] Udeshani KAG, Meegama RGN, Fernando TGI. Statistical feature-based neural network approach for the detection of lung cancer in chest x-ray images. International Journal of Image Processing (IJIP). 2011;**5**(4):425-434

[7] Guan Q, Huang Y, Zhong Z, Zheng Z, Zheng L, Yang Y. Diagnose like a

radiologist: Attention guided convolutional neural network for thorax disease classification. arXiv preprint arXiv:1801.09927 (2018)

[8] Rajpurkar P, Irvin J, Zhu K, Yang B, Mehta H, Duan T, et al. Chexnet: Radiologist-level pneumonia detection on chest x-rays with deep learning. arXiv preprint arXiv:1711.05225 (2017)

[9] Pingale TH, Patil HT. Analysis of cough sound for pneumonia detection using wavelet transform and statistical parameters. In: 2017 International Conference on Computing, Communication, Control and Automation (ICCUBEA). 2017. pp. 1-6 [Online]

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[12] Chan H-P, Sahiner B, Hadjiyski L, Zhou C, Petrick N. Lung nodule detection and classification. U.S. Patent Application 10/504,197, September 22, 2005

#### **Chapter 5**

## Multi-Metric Near-Optimal Image Denoising

*Kenji Hara and Kohei Inoue*

#### **Abstract**

It is necessary to optimize the parameters for each image input to achieve the maximum denoising performance because the performance of denoising algorithms depends largely on the selection of the associated parameters. The commonly used objective image quality measures in quantitatively evaluating a denoised image are PSNR, SSIM, and MS-SSIM, which assume that the original image exists and is fully available as a reference. However, we do not have access to such reference images in many practical applications. Most existing methods for no-reference denoising parameter optimization either use the estimated noise distribution or a unique noreference image quality evaluation measure. In the chapter, for BM3D, which is a state-of-the-art denoising algorithm, we introduce a natural image statistics (NIS) based on the generalized Gaussian distribution (GGD) and the elastic net regularization (EN) regression method and propose its use to perform the BM3D parameter optimization for PSNR, SSIM, and MS-SSIM, respectively, which are the popular image quality evaluation measures, without reference image and knowledge of the noise distribution. Experimental results with several images demonstrate the effectiveness of the proposed approach.

**Keywords:** denoising parameter optimization, BM3D, full-reference image quality, Kullback-Leibler divergence, elastic net regularization regression

#### **1. Introduction**

Image denoising is used for various tasks, such as segmentation, enhancement, frequency decomposition, and local feature extraction. The performance of denoising algorithms generally depends largely on the selection of the parameters. We address the problem of optimizing the parameters of denoising algorithms to achieve maximum performance. The most common image quality evaluation metrics used to quantitatively evaluate the performance of denoising methods include full-reference metrics such as peak signal-to-noise ratio (PSNR), structural similarity index measure (SSIM) [1], and multi-scale structural similarity index measure (MS-SSIM) [2], which assume that the original image exists and is fully available as a reference. However, such reference images are not available in many practical applications. Therefore, noreference image denoising approaches have been intensively developed.

Several methods for optimizing denoising parameters without reference have been proposed that use cross-validation [3, 4] and the L-curve method [5, 6]. These methods are somewhat empirical and hence not necessarily optimization methods in the strict sense. Subsequently, a class of parameter optimization methods [7–9] was developed to minimize an estimate of the mean-squared error (MSE) obtained using Stein's unbiased risk estimate (SURE) [10]. This approach performs PSNR optimization without requiring a reference. Although PSNR is not necessarily a good evaluation measure of image quality, it remains among the most popular objective image quality metrics. However, this SURE-based approach generally necessitates the accurate estimation of the noise variance in the noisy image, which is not trivial.

Recently, Zhu et al. [11] proposed a no-reference optimization method based on a perceptual and no-reference image quality evaluation metric, which requires no knowledge of the noise distribution. Their image quality evaluation metric is very interesting in itself, but is not necessarily widely used. To the best of knowledge, most existing methods for no-reference denoising parameter optimization either use the estimated image noise or individual no-reference image quality evaluation metrics. The only exception is the no-reference parameter optimization method by D'Elia et al. [12], which requires no estimation of noise statistics and achieves its optimality only under the SSIM metric. However, PSNR and MS-SSIM metrics are also widely used for the assessment of image quality. Thus, a denoising algorithm to guarantee the nearoptimality with respect to the non-SSIM criterion, particularly for PSNR and MS-SSIM, is proposed in this chapter. The proposed framework can also easily be extended to incorporate any full-reference image quality measurement metrics that might be discovered in the future.

In the chapter, we propose a novel technique for no-reference parameter optimization in the BM3D denoising algorithm, which is the current state-of-the-art denoising method. Our method adaptively depends on which of the following most widely used full-reference image quality evaluation metrics is optimized: PSNR, SSIM, and MS-SSIM, and requires no knowledge of the noise distribution. To do so, we introduce a natural image statistics (NIS) model based on the generalized Gaussian distribution (GGD) and an elastic net regularization regression model. The pipeline of our method is illustrated in **Figure 1**. Experimental results using SIDBA images are presented to show the effectiveness of the proposed method.

The reminder of chapter is organized as follows. In Section 2, we describe a statistical model of natural images in the wavelet transform domain. In Section 3, we formulate a minimization problem of a statistical distance measure to estimate the optimal parameters under the SSIM and MS-SSIM metrics. In Section 4, we derive a regression-based bias correction procedure to estimate the optimal parameter under the PSNR metric by refining a quasi-optimal parameter. In Section 5, we

**Figure 1.** *Pipeline of our method.*

present experimental results obtained by applying the proposed framework to each state-of-the-art denoising method. Section 5 concludes the chapter.

#### **2. Statistical model of natural images**

In this section, we use a slight modification of Mallat's statistical model of natural images [13] based on generalized Gaussian modeling in the wavelet transform domain. The generalized Gaussian distribution (GGD) [14] refers to a family of symmetric distributions, which includes the Gaussian, the Laplacian, and the uniform distributions as special cases. Recently, GGD has been successfully used in the fields of pattern recognition and image processing, in applications such as texture retrieval [15], digital watermarking [16], face recognition [17], and image segmentation [18–20].

The probability density function (pdf) of GGD with a mean zero is given by

$$p(\mathbf{x}; a, \beta) = \frac{\beta}{2a\Gamma(\mathbf{1}/\beta)} e^{-|\mathbf{x}/a|^{\beta}},\tag{1}$$

where *α* and *β* are, respectively, the scale and shape parameters (GGD parameters) and <sup>Γ</sup>ð Þ¼ *<sup>z</sup>* <sup>Ð</sup> <sup>∞</sup> <sup>0</sup> *e*�*<sup>t</sup> t <sup>z</sup>*�<sup>1</sup>*dt z*ð Þ <sup>&</sup>gt;<sup>0</sup> is the gamma function. For *<sup>β</sup>* <sup>¼</sup> 2, Eq. (2) is equivalent to the Gaussian distribution, whereas for *β* ¼ 1, it is equivalent to the Laplace distribution. When *β* ! 0þ, Eq. (2) becomes a Dirac delta function distribution, and when *β* ! þ∞, the distribution converges to a uniform distribution, as shown in **Figure 2**, and when *β* ! þ∞, the distribution converges to a uniform distribution. The maximum-likelihood estimation (MLE) [21, 22], moment-based [23], and global convergence (GCM) [24] methods are widely used to estimate the GGD parameters ð Þ *α*, *β* . As described below, a statistical feature for natural image is described as a set of the estimated parameters of GGD from the marginal distribution of multiresolution wavelet coefficients of a given set of training images [25].

In the proposed approach, we first acquire a large number (*K*) of grayscale natural images. We first apply the discrete wavelet transformation (DWT) to each component image to decompose it into high-pass subbands (SB) of three different frequency levels and three different orientations, including horizontal subbands *Hj* � � *<sup>j</sup>*¼1,2,3,

vertical subbands *Vj* � � *<sup>j</sup>*¼1,2,3, diagonal subbands *Dj* � � *<sup>j</sup>*¼1,2,3, and low-pass subbands *A*3, where *j* ¼ 1,2,3 denotes the resolution level of the DWT. Then, for each of the 9ð Þ ¼ 3 � 3 high-pass subband components *Gj* � � *G*¼*H*,*V*,*D* n o *<sup>j</sup>*¼1,2,3, of each image, we generate a normalized histogram (SB histogram) with a bin width *<sup>h</sup>* <sup>¼</sup> <sup>3</sup>*:*5*s=n*1*<sup>=</sup>*3, where

*n* is the number of pixels and *s* is the standard deviation of the pixel values, using Scott's rule [26]. For each of the 9 SB histograms of each image, we estimate the

GGD parameters *α*^ð Þ*<sup>k</sup> Gj* , ^*<sup>β</sup>* ð Þ*k Gj* n o *G*¼*H*,*V*,*D* � � *j*¼1,2,3 , by the MLE method [21, 22], where *k* ¼ 1,⋯,*K* is the image number. Finally, as a learning result from natural images, we obtain a set of GGDs for the 9 SB components whose pdfs are given by

$$p\_{G\_{\vec{\jmath}}}(\mathbf{x}) = f\left(\mathbf{x}; \overline{a}\_{G\_{\vec{\jmath}}}, \overline{\beta}\_{G\_{\vec{\jmath}}}\right), \tag{2}$$

where *f*ð Þ �; � , � is the pdf of GGD defined by Eq. (2). *αGj* and *βGj* are respectively the mean values of the total number *K* of the estimated *α* and *β* parameters for each SB component; that is,

$$
\overline{a}\_{\mathcal{G}\_{\mathcal{j}}} = \frac{1}{K} \sum\_{k=1}^{K} \widehat{a}\_{\mathcal{G}\_{\mathcal{j}}}^{(k)}, \quad \overline{\beta}\_{\mathcal{G}\_{\mathcal{j}}} = \frac{1}{K} \sum\_{k=1}^{K} \widehat{\beta}\_{\mathcal{G}\_{\mathcal{j}}}^{(k)}. \tag{3}
$$

#### **3. Parameter quasi-optimization**

In the study, we address the problem of optimizing the parameters of the BM3D algorithm (block-matching and 3D filtering) [27]. The BM3D algorithm is designed to denoise images corrupted with zero-mean additive Gaussian noise. A modified version called SAR-BM3D has also been proposed, which assumes multiplicative speckle noise.

Firstly, the algorithm divides a noisy image into blocks. The similar blocks are stacked together to form a 3D array. Then, based on the structural similarity in each group, collaborative filtering and weighted averaging are carried out. The BM3D algorithm requires that an associated parameter *σ* be set to the noise variance of the image. However, accurate estimation of the noise distribution present in an image is not trivial. In addition, such an optimal denoising parameter generally varies depending on the selection of evaluation criteria.

Here, we consider that the quasi-optimal parameter *σ* is obtained as the value of *σ* selected such that a statistical difference between the set of SB histograms of the denoised image using BM3D algorithm and the set of GGD pdfs is minimized. We adopt as the Kullback-Leibler divergence (KLD) [28] as one of the most widely used statistical measures. We solve the following optimization problem.

$$\overline{\sigma} = \operatorname\*{argmin}\_{\sigma} \sum\_{j=1}^{3} \sum\_{G \in \{H, \, V, \, D\}} D\_{KL} \left( P\_{G\_j} \parallel Q\_{G\_j}(\sigma) \right), \tag{4}$$

where *DKL PGj* k*QGj* ð Þ Θ � � denotes the KLD between two distributions *PGj* and *QGj* ð Þ Θ as

*Multi-Metric Near-Optimal Image Denoising DOI: http://dx.doi.org/10.5772/intechopen.106710*

$$D\_{\rm KL}\left(P\_{G\_{\vec{\gamma}}} \| \big| Q\_{G\_{\vec{\gamma}}}(\sigma)\right) = \sum\_{i} p\_{G\_{\vec{\gamma}}}(\mathbf{x}\_{i}) \log \frac{p\_{G\_{\vec{\gamma}}}(\mathbf{x}\_{i})}{Q\_{G\_{\vec{\gamma}}}(i \mid \sigma)},\tag{5}$$

where *xi* and *QGj* ð Þ *i*j*σ* ð Þ *G* ¼ *H*, *V*, *D*; *j* ¼ 1,2,3 are the center and the value of the *i*-th bin in each SB histogram of the denoised image using BM3D algorithm, respectively. *pGj* ð Þ� ð Þ *G* ¼ *H*, *V*, *D*; *j* ¼ 1,2,3 is the GGD pdfs defined in Eq. (3).

However, the quasi-optimal parameter *σ* did not necessarily achieve an optimal denoising in some evaluation criteria. Thus, we used a paired *t* test at a significance level of *α* ¼ 0*:*05, to determine whether there was a statistically significant difference between the quasi-optimal parameter *σ* and each of *σ* <sup>∗</sup> PSNR, *σ* <sup>∗</sup> SSIM, and *σ* ∗ MS�SSIM, which denote the ground-truth optimal parameters for the popular image quality evaluation metrics PSNR, SSIM, and MS-SSIM, respectively. As described in Section 5, our experimental results suggest that there is a statistically significant difference in only PSNR between the quasi-optimal and ground-truth optimal parameters. Thus, hereinafter we assume that both of the estimated SSIM-optimal parameter *σ*^SSIM and the estimated MS-SSIM-optimal one *σ*^MS�SSIM are given by the quasi-optimal parameter *σ* and that there was a bias between the ground-truth PSNR-optimal parameter *σ* <sup>∗</sup> PSNR and *σ*. In the next section, we describe a method to correct the bias to obtain the estimated PSNR-optimal parameter *σ*^PSNR.

#### **4. Regression-based bias correction**

We generate *N* training pairs of noisy and noise-free images by adding zero-mean Gaussian noise of different levels of noise variance and different random seed numbers to original images. Let *yi* � � PSNR ð Þ *i* ¼ 1, ⋯, *N* (the subscript PSNR is omitted henceforth for brevity) be the objective variable that is the ground-truth PSNR-optimal parameter *σ* <sup>∗</sup> PSNR for the *<sup>i</sup>*-th training pair. Let *<sup>x</sup><sup>i</sup>* <sup>¼</sup> *xi*, *<sup>x</sup>*<sup>2</sup> *<sup>i</sup>* , ⋯, *x p i* � �<sup>T</sup> ð Þ *<sup>i</sup>* <sup>¼</sup> 1, <sup>⋯</sup>, *<sup>N</sup>* be the explanatory variable vector, where *xi* is the estimated quasi-optimal parameter *σ* from the *i*-th noisy image. Let *ξ*<sup>0</sup> ð Þ , *ξ* PSNR be the regression parameter, where *ξ*<sup>0</sup> ∈ and � �<sup>T</sup>

$$\mathfrak{g}\_{\cdot} = \left(\xi\_1, \xi\_2, \dots, \xi\_p\right)^{\cdot} \in \mathbb{R}^p.$$

Ordinary least squares regression is commonly used to perform polynomial regression. Least squares regression is a simple method, but it is widely known that a more stable and interpretable solution is obtained by incorporating regularization into the solution of ordinary least squares. In such regularization regression models, lasso regression is a typical and well-known approach to impose a L1 norm penalty [29]. However, if there are training samples with high correlation as the noisy training images in our learning system, lasso tends to select only one sample and ignore others. Therefore, the bias correction described in this section is achieved with an elastic net [30], which is a robust regression model and avoids this problem. Using the elastic net regularization regression, the regression parameter is obtained by solving the following optimization problem.

$$\left\{\hat{\xi}\_{0},\hat{\xi}\right\} = \operatorname\*{argmin}\_{\left(\xi\_{0},\ \xi\right) \in \mathbb{R}^{p+1}} \sum\_{i=1}^{N} \left(y\_{i} - \xi\_{0} - \mathbf{x}\_{i}^{T}\xi\_{i}\right)^{2} + P\_{\lambda}(\xi),\tag{6}$$

where the regularization term *Pλ*ð Þ*ξ* is expressed as a linear combination of the L1 norm ∥*ξ*∥<sup>1</sup> and the L2 norm ∥*ξ*∥<sup>2</sup> <sup>2</sup> as

$$P\_{\lambda}(\boldsymbol{\xi}) = \lambda\_1 \|\boldsymbol{\xi}\|\|\_1 + \lambda\_2 \|\boldsymbol{\xi}\|\|\_2^2 = \lambda\_1 \sum\_{j=1}^p |\xi\_j| + \lambda\_2 \sum\_{j=1}^p \xi\_j^2,\tag{7}$$

where *λ*<sup>1</sup> and *λ*<sup>2</sup> are the positive magnitudes of the L1 and L2 norm penalties, respectively. By using the solutions of Eq. (7), the estimated PSNR-optimal parameter *σ*^P*SNR* is expressed as follows.

$$
\hat{\sigma}\_{\text{PSNR}} = \overline{\sigma} + \sum\_{j=0}^{p} \left( \hat{\xi}\_{j} \right)\_{\text{PSNR}} \overline{\sigma}^{j}. \tag{8}
$$

Note that for correctness the subscript PSNR is shown explicitly in Eq. (8). In our experiments, we used the degree *p* of the polynomial as *p* ¼ 3 and the tuning parameter *λ* of the elastic net as *λ*<sup>1</sup> ¼ *λ*<sup>2</sup> ¼ 5.

#### **5. Experimental results**

*K* ¼ 6000 training images described in Section 3 were randomly selected from photography websites such as http://pro.foto.com and http://sozaing.com. All the images were cropped to be the size of 256 � 256 pixels. **Figure 3(a, b, c)** shows the plots of the KLD (red curves, left vertical axes) and PSNR, SSIM and MS-SSIM (blue curves, right vertical axes) for different values of the BM3D parameter *σ* (horizontal axes) for the Lena image corrupted by Gaussian noise *N*ð Þ 0, 30 , respectively. From **Figure 3**, it may be observed that the quasi-optimal parameter *σ*, which is the value of *σ* minimizing KLD, was slight smaller than the ground-truth PSNR-optimal parameter *σ* ∗ PSNR, whereas *σ* was almost equal to the ground-truth SSIM-optimal and MS-SSIMoptimal parameters *σ* <sup>∗</sup> SSIM and *σ* <sup>∗</sup> MS�SSIM.

Next, a total of 50ð Þ ¼ 5 � 5 � 2 noisy SIDBA images (Lena, Pepper, Airplane, Parrots, and Girl) corrupted by five different zero-mean Gaussian noise *N*ð Þ 0, *σ<sup>n</sup>* ,ð Þ *σ<sup>n</sup>* ¼ 10, 20, ⋯, 50 for different two seeds of random number generator were prepared as training images, and then, the regularization regression described in Section 4 was applied on the training image set to determine the relationships between the quasi-optimal parameter *σ* and each of the ground-truth optimal parameters *σ* <sup>∗</sup> PSNR, *σ* <sup>∗</sup> SSIM, and *σ* <sup>∗</sup> MS�SSIM.

#### **Figure 3.**

*Plots of KLD (red curves) and popular image quality evaluation metrics (blue curves) versus different BM3D parameters σ. (a) KLD and PSNR. (b) KLD and SSIM. (c) KLD and MS-SSIM.*

*Multi-Metric Near-Optimal Image Denoising DOI: http://dx.doi.org/10.5772/intechopen.106710*

**Figure 4.**

*Plots of ground-truth optimal parameters versus different quasi-optimal parameters σ. (a) σ* <sup>∗</sup> PSNR *versus σ. (b) σ* ∗ SSIM *versus σ. (c) σ* <sup>∗</sup> MS�SSIM *versus <sup>σ</sup>.*

To this end, first we qualitatively evaluated the denoising parameter quasi-optimization described in Section 3. **Figure 4(a, b, c)** shows the plots of the ground-truth optimal parameters *σ* <sup>∗</sup> PSNR, *σ* <sup>∗</sup> SSIM, and *σ* <sup>∗</sup> MS�SSIM (vertical axes) versus the quasi-optimal parameter *σ* (horizontal axes), respectively. From **Figure 4(a)**, it may be observed that *σ* is smaller than *σ* <sup>∗</sup> PSNR and the trend becomes more significant for larger noise variance. In contrast, from **Figure 4(b, c)**, it may be observed that *σ* was very close to both of *σ* <sup>∗</sup> SSIM and *σ* <sup>∗</sup> MS�SSIM. Furthermore, to quantitatively evaluate the denoising parameter quasi-optimization, we used a paired *t* test at a significance level of *α* ¼ 0*:*05 to compare the quasi-optimal parameter *σ* with each of the ground-truth optimal parameters *σ* <sup>∗</sup> PSNR, *σ* <sup>∗</sup> SSIM, and *σ* <sup>∗</sup> MS�SSIM. The results showed no statistically significant differences for SSIM (the paired *t* test yielded a *p* value of 0*:*1167 >0*:*05) and MS-SSIM (the paired *t* test gives a *p* value of 0*:*1744>0*:*05), and hence, we estimate the SSIM-optimal and MS-SSIM-optimal parameters as *σ*^SSIM ¼ *σ*^MS�SSIM ¼ *σ*. In contrast, the above results showed a statistically significant difference for PSNR (the paired *<sup>t</sup>* test gives a *<sup>p</sup>* value of 5*:*<sup>2962</sup> � <sup>10</sup>�<sup>8</sup> <sup>&</sup>lt; <sup>0</sup>*:*05), and thus, we calculated Eq. (8) to find the estimated PSNR-optimal parameter *σ*^PSNR.

To qualitatively evaluate the parameter optimization described in Section 4, we illustrate in **Figure 5(a)** the plots of the ground-truth PSNR-optimal parameter *σ* <sup>∗</sup> PSNR (vertical axis) versus the quasi-optimal parameter *σ* (blue plots, horizontal axis) and the estimated PSNR-optimal parameter *σ*^PSNR (red plots, horizontal axis) for the

#### **Figure 5.**

*Plots of ground-truth PSNR-optimal parameters σ* <sup>∗</sup> PSNR *versus different quasi-optimal parameters σ (blue points) and estimated PSNR-optimal parameters σ*^PSNR *(red points) on the training and test image sets. (a) The training image set. (b) The test image set.*

training image set. From **Figure 5(a)**, it may be observed that bias correction based on the elastic net regularization regression improved the quasi-optimal parameters. To quantitatively evaluate the parameter optimization described in Section 4, we used a paired *t* test at a significance level of *α* ¼ 0*:*05 to compare the estimated PSNRoptimal parameter with the ground-truth PSNR-optimal parameter. The results showed no statistically significant differences (the paired *t* test gives a *p* value of *p* ¼ 0*:*2692 >0*:*05).

In **Tables 1** and **2**, we summarize the pairs of the ground-truth optimal parameters and the metric values and the pairs of the estimated optimal parameters and the


**Table 1.**

*Comparison of the ground-truth optimal parameters, the ground-truth metric values, the estimated optimal parameters, and the estimated metric values. The comparisons are shown for the training image set.*

*Multi-Metric Near-Optimal Image Denoising DOI: http://dx.doi.org/10.5772/intechopen.106710*


#### **Table 2.**

*Comparison of the ground-truth optimal parameters, the ground-truth metric values, the estimated optimal parameters, and the estimated metric values. The comparisons are shown for the test image set.*

metric values for different levels of zero-mean Gaussian noise variance and different metrics for the training image set and a test image set consisting of four SIDBA images (Balloon, Couple, Earth, and Barbara; hereinafter are referred to as "the testing image set"), respectively.

In **Figure 5(b)**, we show the plots of the ground-truth PSNR-optimal parameter (vertical axis) versus the quasi-optimal parameter (blue plots, horizontal axis) and the estimated PSNR-optimal parameter (red plots, horizontal axis) for the test image set. From **Figure 5(b)**, as well as the results in **Figure 5(a)**, our bias correction visually improves the quasi-optimal parameters. As in **Figure 5(a)**, we used a paired *t* test at a significance level of *α* ¼ 0*:*05 to compare the estimated PSNR-optimal parameter with the ground-truth PSNR-optimal parameter. The results showed no statistically significant differences (the paired *t* test gives a *p* value of *p* ¼ 0*:*1920>0*:*05), and hence, we can confirm the validity of *σ*^PSNR.

**Figure 6** illustrates a visual comparison of the denoising results. **Figure 6(a)** shows the standard Barbara image. **Figure 6(b)** shows the enlarged detail in the eye

#### **Figure 6.**

*Visual comparison of denoising results. (a) Barbara image. (b) Enlarged detail of (a). (c) Image corrupted by Gaussian noise N*ð0,*σ<sup>n</sup>* ¼ 30*). (d) Enlarged detail of (c). (e) Denoised image with the BM3D algorithm the parameter σ of which is the estimated noise variance from (c) (σ*^*<sup>n</sup>* ¼ 20*:*6*). (f) Denoised image with the BM3D algorithm the parameter σ of which is the estimated PSNR-optimal parameter σ*^PSNR ¼ 33*:*3*. (g) Denoised image with the BM3D algorithm the parameter σ of which is the estimated SSIM-optimal parameter σ*^SSIM ¼ 28*:*6*. (h) Denoised image with the BM3D algorithm the parameter σ of which is the estimated MS-SSIM-optimal parameter σ*^MS�SSIM ¼ 28*:*6*. (i) Enlarged detail of (e). (j) Enlarged detail of (f). (k) Enlarged detail of (g). (l) Enlarged detail of (h).*

*Multi-Metric Near-Optimal Image Denoising DOI: http://dx.doi.org/10.5772/intechopen.106710*

**Figure 7.**

*Plots of image quality evaluation metric values versus different levels of image noise variance for the direct estimation of the image noise variance (blue lines and points), our proposed method (red lines and points), and the ground-truth (black lines and points). The comparisons are shown for the test image set. (a) PSNR. (b) SSIM. (c) MS-SSIM.*

area of the original Barbara image shown in (a). **Figure 6(c)** shows the noisy Barbara image corrupted by additive zero-mean Gaussian noise *N*ð Þ 0, *σ<sup>n</sup>* ¼ 30 . **Figure 6(d)** shows an enlarged detail in (c). **Figure 6(e)** shows the denoised image by the BM3D with the directly estimated noise variance from the noisy Barbara image shown in (c) as the parameter value. **Figure 6(f, g, h)** shows the denoised images by the BM3D with the estimated PSNR-optimal, SSIM-optimal and MS-SSIM-optimal parameters, respectively. **Figure 6(i–l)** shows the enlarged details in (e), (f), (g), and (h), respectively. These results indicate that the BM3D model was able to denoise the noisy image with reasonable accuracy by using our estimated optimal parameters.

Finally, for each of the image quality evaluation metrics PSNR, SSIM, and MS-SSIM, we compare the measure value of the BM3D denoised image using our estimated optimal parameters, against that using the estimated noise variance from the input noisy image. **Figure 7(a, b, c)** shows the plots of the mean values of PSNR, SSIM, and MS-SSIM at each noise variance across the test image set, respectively. From these results, it may be observed that the BM3D algorithm with our estimated optimal parameter outperformed that with the directly estimated noise variance from the input images.

#### **6. Conclusions**

We addressed the problem of estimating the optimal parameter of state-of-the-art denoising algorithm BM3D algorithm without any reference and without any knowledge of the noise distribution, adaptively depending on which of the following widely used image quality evaluation metrics are optimized: PSNR, SSIM, and MS-SSIM. The proposed method for SSIM and MS-SSIM optimization is formulated as a minimization problem for a Kullback-Leibler divergence measure based on the natural image statistics and generalized Gaussian distribution based prior. The method for PSNR optimization is formulated as a combination of the above optimization and an elastic net regression, which provides a very robust regression model. From our experimental results, we have confirmed that the proposed statistical measure and robust regression approach can be used to optimize the denoising parameter of the BM3D algorithm.

*Denoising – New Insights*

#### **Author details**

Kenji Hara\*† and Kohei Inoue† Department of Media Design, Kyushu University, Fukuoka, Japan

\*Address all correspondence to: hara@design.kyushu-u.ac.jp

† These authors contributed equally.

© 2022 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

*Multi-Metric Near-Optimal Image Denoising DOI: http://dx.doi.org/10.5772/intechopen.106710*

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#### **Chapter 6**

## Perspective Chapter: New Image Denoising Approach Based on SWT and 2-D Dual-Tree Discrete Wavelet Transform

*Mourad Talbi and Riadh Baazaoui*

#### **Abstract**

In this chapter, we propose a new image denoising approach. It consists in applying a Stationary Wavelet Transform (SWT) based image denoising technique, in the domain of 2‐D Dual-Tree Discrete Wavelet Transform. In fact, this proposed approach consists first of applying the 2‐D Dual-Tree Discrete Wavelet Transform to the noisy image. Then, the obtained noisy wavelet coefficients are denoised by applying to each of them a SWT based image denoising technique. Finally, the denoised image is reconstructed by applying the inverse of the 2‐D Dual-Tree Discrete Wavelet Transform to the obtained denoised wavelet coefficients. For applying this SWT based image denoising technique, we use soft thresholding, the Daubechies 4 as the mother wavelet and the decomposion level is equal to 5. The performance of this proposed image denoising approach, is pouved by the results obtained from the computations of PSNR (Peak Signal-to-Noise Ratio) and SSIM (Structural Similarity).

**Keywords:** image denoising, 2-D dual-tree discrete wavelet transform, SWT-2D, PSNR, SSIM, standard deviation

#### **1. Introduction**

Noisy images frequently arise in the high-level vision tasks and this makes image denoising becoming an important task in the low-level vision domain [1]. For example, take a given denoising model:

$$y = \mathfrak{x} + \mathfrak{n} \tag{1}$$

With *x*, *y* and *n* are respectively the clean images, the given noisy image and the Additive Gaussian Noise (AWGN) having *σ* as standard deviation [1]. There are diverse approaches for reducing noise that various researchers have done. Each of these approaches owns its advantages and disadvantages. In [2], a review of some significant work in the domain of image denoising based on the denoising techniques were presented. These techniques can be classified as wavelet domain,

spatial domain, or both techniques can combine for obtaining an advantage of them. In the medical domain, Mittal et al. [3] have presented a methodology for improving and eliminating the high noise of the medical image employing the Stationary Wavelet Transform (SWT) technique. In their work, an efficient and simple approach for adaptive noise elimination was used, the SWT-2D denoising method on the medical image that is degraded by noise. In this chapter, we propose a novel approach of Image denoising. It consists in applying a Stationary Wavelet Transform (SWT) based image denoising technique [4] in the domain of 2-D Dual-Tree Discrete Wavelet Transform. This SWT-based image denoising technique [4] is based on soft thresholding of the noisy wavelet coefficients obtained from the noisy image decomposition using the SWT-2D. For this decomposition, we use Daubechies 4 as the mother wavelet and the level is equal to 5. Those choices are the same as those in ref. [4].

This proposed denoising approach is completely different from the other denoising technique based on thresholding in the domain of 2-D Dual-Tree Complex Wavelet Transform [5]. In fact, this difference lies in the fact that we apply SWT-based image denoising technique [4] not to the noisy image to be denoised, but to each noisy wavelet coefficient obtained from the application of this Transform [5] to this image. Consequently, this idea can introduce more adaptability compared to the application of this technique based on thresholding in the domain of 2-D Dual-Tree Discrete Wavelet Transform [5], to this image.

The remaining of this chapter is organized as follows: in Section 2, we will deal with 2-D Dual-Tree Complex Wavelet Transform [5]. In Section 3, we will deal with the SWT-2D-based image denoising technique [4]. In Section 4, we will detail the image-denoising approach proposed in this work. In Section 5, we will present results and discussion and we will conclude in Section 6.

#### **2. 2-D dual-tree complex wavelet transform**

It turns out that, for some applications of *DWT* (Discrete Wavelet Transform), ameliorations can be obtained by employing an expansive wavelet transform in place of a critically sampled one [5]. An expansive transform is one that permits to convert an *N*-point signal into *M* coefficients with *M* > *N*. There are numerous sorts of expansive DWTs; here is described the dual-tree complex *DWT* [5, 6]. The dual-tree complex *DWT* of a signal *x* is implemented employing two critically sampled DWTs in parallel on the same data, as illustrated in **Figure 1**.

The transform is 2-times expansive because for an N-point signal, it permits to have 2*NDWT* coefficients. If the filters in the upper and lower DWTs are the same, consequently no advantage is added. Though, when the filters are designed in a specific way, consequently the sub-band signals of the upper *DWT* can be considered as the real part of a complex wavelet transform, and sub-band signals of the lower *DWT*can be viewed as the imaginary part. Equivalently, for specially designed filters sets, the wavelet associated with the upper *DWT* can be viewed as an approximate Hilbert transform of the wavelet associated with the lower DWT. When designed in this manner, the dual-tree complex *DWT* is approximately shift-invariant, in contrast with the critically sampled DWT. Furthermore, the dual-tree complex DWT can be employed for implementing 2-D wavelet transforms where each wavelet is oriented, which is precisely useful for image processing. For the separable 2–D DWT, recall that *Perspective Chapter: New Image Denoising Approach Based on SWT and 2-D Dual-Tree Discrete… DOI: http://dx.doi.org/10.5772/intechopen.112103*

**Figure 1.** *The dual-tree complex DWT.*

**Figure 2.** *Complex 1-D wavelet, ψ*ð Þ*t [5, 6].*

one of the three wavelets does not own a dominant orientation. The dual tree complex DWT outperforms the critically sampled *DWT* for applications such as image denoising and enhancement. The complex wavelet associated with the dual-tree complex DWT is illustrated in **Figure 2**. For determining the real part of the complex wavelet, we set all coefficients to zero, except for one coefficient in the upper DWT, and after that applying the inverse transform. For determining the imaginary part, the exception is a single coefficient in the lower DWT.

#### **3. A stationary wavelet transform (SWT) based image denoising technique**

The SWT (Stationary Wavelet Transform) [7, 8] is similar to the Discrete Wavelet Transform (DWT) except the signal is never sub-sampled and instead the filters are up sampled at each level of decomposition [7]. Each level's filters are up-sampled versions of the previous as shown in **Figure 3**.

The SWT is an inherent redundant scheme, as each set of coefficients contains the same number of samples as the input. So for a decomposition of *N* levels, there is a redundancy of **2***N*.

An image denoising technique based on thresholding in the SWT domain, is applied in our denoising system proposed in this work. This technique can be summarized by the block diagram illustrated at **Figure 4**.

According to **Figure 4**, the Stationary Wavelet Transform 2D (SWT–2*D*) is firstly applied to the noisy image, *Ib*, in order to obtain noisy stationary wavelet coefficients. Those obtained coefficients are then denoised by employing soft thresholding and finally the inverse of SWT–2*D*, *SWT*<sup>1</sup> <sup>2</sup>*<sup>D</sup>* is applied to the obtained thresholded coefficients for having the denoised image, *Id*.

**Figure 3.** *(a) Wavelet decomposition tree, (b) SWT filters [7].*

#### **Figure 4.**

*The block diagram of an image denoising technique based on thresholding in the SWT domain.*

*Perspective Chapter: New Image Denoising Approach Based on SWT and 2-D Dual-Tree Discrete… DOI: http://dx.doi.org/10.5772/intechopen.112103*

#### **4. The proposed image denoising approach**

As previously mentioned, in this work, we propose a new image denoising approach. It consists in applying a SWT based image denoising technique [4] in the domain of 2-D Dual-Tree Discrete Wavelet Transform [5]. In fact, this proposed approach consists firstly in applying the 2-D Dual-Tree Discrete Wavelet Transform to the noisy image and the obtained noisy wavelet coefficients are then denoised by applying to each of them, a SWT based image denoising technique [4]. Finally, the denoised image is reconstructed by applying the inverse of the 2-D Dual-Tree Discrete Wavelet Transform to the obtained denoised wavelet coefficients. This proposed image denoising approach can be summarized by the block diagram illustrated at **Figure 5**.

According to **Figure 5**, the 2-D dual-Tree Discrete Wavelet Transform is firstly applied to the noisy image, *Ib* in order to obtain noisy wavelet coefficients, *Wb j* f gf g*s* , 1≤ *j*≤2, 1≤*s*≤3. Each of those coefficients is then denoised by applying a technique of image denoising based on thresholding in SWT domain [4] and we obtain denoised wavelet coefficients, *Wd j* f gf g*s* , 1≤*j*≤ 2, 1≤*s* ≤3. To those denoised coefficients, is applied the inverse of the 2-D dual-Tree Discrete Wavelet Transform in order to have finally the denoised *Id*.

As previously mentioned, for the application of the denoising technique based on thresholding in the SWT domain, is used Daubechies 4 as the mother wavelet. Moreover, the decomposition level is equal to 5. Those choices are the same to those in [4]. Those choices are justified by the fact that in our comparative study, we want to use the same mother wavelet and the same decomposition level such as used in [4].

#### **5. Results and discussion**

In this section, we will present the results obtained from the computations of Peak Signal to Noise Ratio (PSNR) and Structural Similarity (SSIM). Those results are obtained from the application of the proposed image denoising approach, the denoising


**Figure 5.** *The block diagram of the proposed image denoising approach.*

technique based on thresholding in the SWT domain [4], the image denoising technique based on thresholding in the domain of 2-D Dual-Tree Discrete Wavelet Transform [5] and the image denoising approach using deep neural network [9].

In the following sub-section we will present the previously mentioned evaluation criterion, which are the PSNR and the SSIM. The PSNR is a better test since it takes the signal strength into consideration (not only the error). The PSNR and SSIM are expressed as follow [10]:

$$\text{SSIM} = \frac{\left(2\mu\_{\text{x}}\mu\_{\text{y}} + c\_1\right)\left(2\sigma\_{\text{xy}} + c\_2\right)}{\left(\mu\_{\text{x}}^2 + \mu\_{\text{y}}^2 + c\_1\right)\left(\sigma\_{\text{x}}^2 + \sigma\_{\text{y}}^2 + c\_2\right)}\tag{2}$$

Where *σ*, *σxy* and *μ* are respectively the variance, the covariance of the image and *c*<sup>1</sup> and *c*<sup>2</sup> are the stabilizing constants. The SSIM value is generally between 0 and 1 and similar images have value of SSIM near to 1.

$$PSNR = 10 \bullet \log\_{10} \left( \frac{MAX\_l^2}{MSE} \right) \tag{3}$$

With MSE is the Mean Square Error, expressed as follow:

$$\text{MSE} = \frac{1}{n} \sum\_{i=1}^{n} \left( \mathbf{X}\_i - \mathbf{X}\_i^\* \right)^2 \tag{4}$$

The MSE is one of the earliest tests which performed to test whether two images are similar.

As previously mentioned, those results (**Table 1**) are in terms of PSNR and SSIM and they are obtained for different images and diverse values of level (*σ*Þ of noise



*Perspective Chapter: New Image Denoising Approach Based on SWT and 2-D Dual-Tree Discrete… DOI: http://dx.doi.org/10.5772/intechopen.112103*

#### **Table 1.**

*Results obtained in terms of PSNR and SSIM.*

corrupting the original image (clean image). This noise is an Additive Gaussian White Noise (AGWN).

In **Figure 6**, are illustrated some examples of image denoising by applying the denoising approach proposed in this work and the other previously mentioned techniques, used in our evaluation [4, 5, 9]. According to **Figure 6**, the noise is

#### **Figure 6.**

*An example of image denoising: (a) clean image, (b) Noisy image (σ* ¼ 20*), (c) Denoised image obtained by applying the proposed technique (PSNR = 30.6924), (d) Denoised image obtained by applying* deep learning *(PSNR = 22.4978), (e) Denoised image obtained by applying soft thresholding in the SWT domain (PSNR = 30.1884) (f) Denoised image obtained by applying soft thresholding in the domain of 2-D dual-tree discrete wavelet transform (PSNR = 30.2840).*

*Perspective Chapter: New Image Denoising Approach Based on SWT and 2-D Dual-Tree Discrete… DOI: http://dx.doi.org/10.5772/intechopen.112103*

considerably reduced while preserving the original image and this precisely when applying the image denoising approach proposed in this work.

According to **Table 1**, the best results are highlighted in purple color and they are practically obtained by applying the proposed image denoising approach. Consequently, this proposed approach outperforms the other three techniques [4, 5, 9], used for our evaluation.

#### **6. Conclusion**

In this chapter, we proposed a new image denoising approach. It consists in applying a Stationary Wavelet Transform (*SWT*) based image denoising technique [4] in the domain of 2–*D* Dual-Tree Discrete Wavelet Transform. In fact, this proposed approach consists firstly in applying the 2–*D* Dual-Tree Discrete Wavelet Transform to the noisy image and the obtained noisy wavelet coefficients are then denoised by applying to each of them a *SWT* based image denoising technique [4]. Finally, the denoised image is reconstructed by applying the inverse of the 2–*D* Dual-Tree Discrete Wavelet Transform to the obtained denoised wavelet coefficients. The performance of this proposed image denoising approach, is proved by the results obtained from the computations of PSNR (Peak Signal-to-Noise Ratio) and SSIM (Structural Similarity). In fact, it permits to obtain the best values of PSNR and SSIM compared to three other image denoising techniques existing in literature. These three techniques are as follows: the Image denoising approach based on neural network [9], the denoising technique based on thresholding in the *SWT* domain [4], and the denoising approach based on thresholding in the domain of 2-DDual-Tree Discrete Wavelet Transform [5]. For example, when the noisy image is Noisy House.tif with standard deviation of Additive Gaussian White Noisen, (*σ* ¼ 20Þ, the proposed denoising approach permits to obtain *PSNR* ¼ **30***:***7882** and *SSIM* ¼ **0***:***8462**. However, the denoising technique based on thresholding in the SWT domain [4], permits to obtain *SNR* ¼ 30*:*3082 and *SSIM* ¼ 0*:*7360. The denoising technique based on deep learning [9], permits to obtain *PSNR* ¼ 22*:*4921 and *SSIM* ¼ 0*:*3090. The denoising technique based on thresholding in the domain of 2-D Dual-Tree Discrete Wavelet Transform [5], permits to obtain *PSNR* ¼ 30*:*5116 and *SSIM* ¼ 0*:*7766. Consequently, this example shows clearly the superiority of the proposed denoising approach compared to the other three techniques existing in literature [4, 5, 9]. The main drawbak of this proposed image denoising approach is its computation complexity compared to the two other denoising techniques [4, 5]. This complexity is due to the fact that we apply the *SWT* based image denoising technique [4] not to the whole noisy image but we apply this technique [4] to each noisy coefficient obtained from the application of the 2–D Dual-Tree Discrete Wavelet Transform, to the noisy image. Moreover, in this proposed denoising approach, we use two completely different wavelet transforms which are the Stationary Wavelet Transform (SWT) and the 2–D Dual-Tree Discrete Wavelet Transform. Consequently, we have more computation complexity compared to the two other image denoising techniques [4, 5].

#### **Author details**

Mourad Talbi<sup>1</sup> \* and Riadh Baazaoui<sup>2</sup>

1 LaNSER, Center of Researches and Technologies of Energy of BorjCedria, Tunis, Tunisia

2 Faculty of Sciences of Tunis, Department of Mathematics, Tunisia

\*Address all correspondence to: mouradtalbi196@yahoo.fr

© 2023 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

*Perspective Chapter: New Image Denoising Approach Based on SWT and 2-D Dual-Tree Discrete… DOI: http://dx.doi.org/10.5772/intechopen.112103*

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[3] Mittal N, Raj A, Goyal H. Enhancement and removal of noise from medical images by wavelet transform method. In: 2019 3rd International Conference on Electronics, Communication and Aerospace Technology (ICECA). Coimbatore, India: IEEE Xplore; 2019. pp. 1126-1130. DOI: 10.1109/ICECA.2019.8821979

[4] Generate MATLAB Code for 2-D Sta tionary Wavelet Denoising - MATLAB & Simulink - MathWorks France. Available from: https://www.mathworks.com/ help/wavelet/ug/generating-matlabcode-for-2-d-stationary-waveletdenoising.html

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[6] Patrick L. Ondelettes complexes pour l'analyse des lois d'echelles. Master des Sciences de la Matière, Ecole Normale Supérieure de Lyon Université Claude Bernard Lyon 1; 2006

[7] Al Jumah A. Denoising of an image using discrete stationary wavelet transform and various thresholding techniques. Journal of Signal and Information Processing. 2013;**4**:33-41. DOI: 10.4236/jsip.2013.41004

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[10] Talbi M, Bouhlel MS. Wavelets and LPG-PCA for image denoising, wavelet theory and its applications. 2018. ISBN: 978-1-78923-433-6, DOI: 10.5772/ intechopen.7445

### *Edited by Mourad Talbi*

*Denoising - New Insights* provides a comprehensive overview of signal and image denoising techniques. It also examines and compares the performance of several innovative denoising approaches involving the use of mathematical tools such as wavelets, deep learning, minimum mean square error, and more. This book is a useful resource for engineers and researchers in signal and image processing.

Published in London, UK © 2023 IntechOpen © natasaadzic / iStock

Denoising - New Insights

Denoising

New Insights

*Edited by Mourad Talbi*