A SAR Image Despeckling Method Based on an Extended Adaptive Wiener Filter and Extended Guided Filter

: The elimination of multiplicative speckle noise is the main issue in synthetic aperture radar (SAR) images. In this study, a SAR image despeckling ﬁlter based on a proposed extended adaptive Wiener ﬁlter (EAWF), extended guided ﬁlter (EGF), and weighted least squares (WLS) ﬁlter is proposed. The proposed EAWF and EGF have been developed from the adaptive Wiener ﬁlter (AWF) and guided Filter (GF), respectively. The proposed EAWF can be applied to the SAR image, without the need for logarithmic transformation, considering the fact that the denoising performance of EAWF is better than AWF. The proposed EGF can remove the additive noise and preserve the edges’ information more e ﬃ ciently than GF. First, the EAWF is applied to the input image. Then, a logarithmic transformation is applied to the resulting EAWF image in order to convert multiplicative noise into additive noise. Next, EGF is employed to remove the additive noise and preserve edge information. In order to remove unwanted spots on the image that is ﬁltered by EGF, it is applied twice with di ﬀ erent parameters. Finally, the WLS ﬁlter is applied in the homogeneous region. Results show that the proposed algorithm has a better performance in comparison with the other existing ﬁlters.


Introduction
Despeckling of synthetic aperture radar (SAR) images is one of the main topics of recent studies [1]. SAR images have been widely used in many fields, such as disaster monitoring, environmental, protection, and topographic mapping [1]. It is not even affected by cloud cover or variation in solar illumination. A SAR image is formed by the continuous interaction of emitted microwave radiance with targeted regions, which causes random constructive and destructive noisiness resulting in multiplicative noise called speckle noise. Several methods have been proposed to remove these unwanted patterns, and some noise removal methods are based on spatial filtering, for instance, completely remove speckle noise in the degraded image because both the noise and signal may have a continuous power spectrum. Therefore, denoising is performed through an MMSE filter. We used the AWF for despeckling and improved the AWF structure in order to increase noise reduction efficiency via EAWF. In addition, the main tool in image despeckling is an edge-aware method [25], such as a guided filter (GF). It can be applied as an edge-preserving operator, such as the well-known BF, but functions better near to the edges. In this study, we improved the performance of GF with the proposed edge detection method. The extended guided filter (EGF) outcome shows better speckle noise removal than the GF outcome. We focused on despeckling SAR images using a hybrid combination of EAWF, EGF, and weighted least squares (WLS) filter to make it more efficient. First, the EAWF is applied to the input image. Then, a logarithmic transformation is applied to the resulting EAWF image in order to convert multiplicative noise into additive noise. Next, to remove the additive noise and preserve edge information, EGF is used. Finally, in order to eliminate speckle noise in homogeneous regions, the WLS filter is used (Figure 1). The organization of this study is as follows: The materials and methods are explained in section 2. In section 3, the proposed algorithm is shown. Experimental outcomes and experiments on real SAR images are described in Section 4 and Section 5. Finally, Computational Complexity, Discussion, and the concluding remarks are given in Section 6, Section 7 and Section 8 respectively.

Measurement of Performance
After enhancement, the image quality was measured by comparing it with the noise-free images using some metrics. In section 3, we use six parameters of PSNR, PFOM, SNR, SSIM, IQI, and MAE. In section 5, we use one parameter of the equivalent number of look (ENL) and standard deviation (STD) and in the remaining sections we use two parameters of PSNR and SSIM. PSNR is an engineering term for the ratio between the maximum possible power of a signal and the power of corrupting noise that affects the fidelity

Measurement of Performance
After enhancement, the image quality was measured by comparing it with the noise-free images using some metrics. In Section 3, we use six parameters of PSNR, PFOM, SNR, SSIM, IQI, and MAE. In Section 5, we use one parameter of the equivalent number of look (ENL) and standard deviation (STD) and in the remaining sections we use two parameters of PSNR and SSIM. PSNR is an engineering term for the ratio between the maximum possible power of a signal and the power of corrupting noise that affects the fidelity of its representation. Next, SNR compares the level of the desired signal to the level of background noise and SSIM is a procedure to predict the perceived quality of digital television, cinematic pictures, and other kinds of digital images. In addition, IQI is considered the fourth parameter for assessing the quality of denoised images, and MAE is the average of all absolute errors for measuring the proximity of forecasts or predictions to the eventual outcomes. PFOM is Pratt's figure of merit used here as an assessment criterion for the standard edge detectors.

Adaptive Wiener Filter
One of the first methods developed for denoising in digital images is based on Wiener filtering. If we assume (n 1 , n 2 ) is a particular pixel location, the AWF is given by [26].
where I is the input image, variance (σ 2 ) and mean µ are locally estimated from the set ℵ of (N × M) local neighborhood of each pixel. So that µ = 1 MN n 1 ,n 2 ℵ I(n 1 , n 2 ) (2) In addition, (σ n ) is the variance of the noise.

Guided Filter
GF transforms the output q i for the guidance I k .of the window ω k , and k is the center pixel in the window, as follows: q i = a k I k + b k ∀i ∈ ω k (4) where ω k is a square window with the size of (2r + 1) × (2r + 1) and linear coefficients of a k and b k are constants estimated from the window ω k . Generally, q i = p i − n i (5) where n i and p i define the noise and input image, respectively. The linear coefficients can be estimated by minimizing the squared difference between the input pi and the output qi, as follows: Remote Sens. 2020, 12, 2371 5 of 32 where ε is a normalization parameter. It can serve to prevent a k from becoming immeasurably large. The coefficients b k and a k can be solved by linear regression.
where σ 2 k and µ k are the variance and the mean of the guidance image in the window ω k and |ω| indicates the number of pixels in ω k , and P k = 1 |ω| P i . As ε and the window size ω k adjustment, the noise is deleted and the edge regions are preserved.

Improvement of Adaptive Wiener Filter
In Equation (1), we used the dispersion index instead of the variance. The dispersion index is for determining if a set of observed occurrences are clustered or dispersed. It is defined as the ratio of the variance to the mean.
To enhance performance, a dispersion index is also used to obtain the noise estimate instead of the variance. We can simplify Equation (10) in the form of Equation (11).
In fact, 2 2 ( ( 1 , 2 ) − ) is almost the same as the noise but with a different sign. Meanwhile, speckle noise is a multiplicative noise. Therefore, noise has less of an effect in lower light intensity. By multiplying the mean in 2 2 ( ( 1 , 2 ) − ), a better approximation of noise is obtained ( 2 2 ( ( 1 , 2 ) − ) ). Figure   2 shows the comparison between AWF, homogeneous adaptive Wiener filter (HAWF), and EAWF. To evaluate this method, we compared the EAWF and existing methods with PSNR, SSIM, IQI and Pratt's FOM quantitative measurements ( Figure 3). In this comparison, a 250x250 Lena image is used. To evaluate this method, we compared the EAWF and existing methods with PSNR, SSIM, IQI and Pratt's FOM quantitative measurements ( Figure 3). In this comparison, a 250x250 Lena image is used. To evaluate this method, we compared the EAWF and existing methods with PSNR, SSIM, IQI and Pratt's FOM quantitative measurements ( Figure 3). In this comparison, a 250x250 Lena image is used.

SAR Speckle Noise Model and Logarithmic Transformation
The following model is appropriate for images with multiplicative noise: f(x,y) = g(x,y).ηm(x,y) + ηa(x,y) where f(x,y),g(x,y),ηm(x,y) and ηa(x,y) are the real noisy image, unknown noise-free image, and additive and multiplicative noise functions, respectively. Since additive noise is considered to be less than multiplicative noise, we considered Equation (13) for speckle noise.
f(x,y) = g(x,y).ηm(x,y) where f(x,y) defines the SAR image degraded by speckle noise. g(x,y) indicates a radar scattering characteristic of the ground target (i.e., the noise-free image). ηm(x,y) also defines the speckle due to fading. g(x,y) and ηm(x,y) are independent. ηm(x,y) conforms to a Gamma distribution where the variance is 1 L and the mean is one.
where N ≥ 0, L ≥ 1, and L is the equivalent number of looks (ENL), where a bigger L defines weaker speckling. The noise of the speckles present in images is the noise of multiplicative. Therefore, we preferred to carry out a logarithmic transform of the noisy image and multiplicative noise becomes addictive as it is shown in the following equation [27]: Logf(x,y) = logg(x,y) + ηm(x,y) The coefficient of variation (CV) is determined as a ratio of standard deviation (σ) to the average (µ). Because the CV is unitless, the CV value is similar in extreme variances in regions with high intensity and low variances in regions with lower intensity. This leads to a similar function for regions with different brightness (Figure 4). The formula for CV is defined as follows: Where Sa and ma are the standard deviation and mean, respectively. Therefore, high, low, and intermediate CV values correspond to 'edges', 'homogenous', and 'detail'. and the mean is one.
where N ≥ 0, L ≥ 1, and L is the equivalent number of looks (ENL), where a bigger L defines weaker speckling.
The noise of the speckles present in images is the noise of multiplicative. Therefore, we preferred to carry out a logarithmic transform of the noisy image and multiplicative noise becomes addictive as it is shown in the following equation [27]: Logf(x,y) = logg(x,y) + ƞm(x,y)

Coefficient of Variation
The coefficient of variation (CV) is determined as a ratio of standard deviation (σ) to the average (µ). Because the CV is unitless, the CV value is similar in extreme variances in regions with high intensity and low variances in regions with lower intensity. This leads to a similar function for regions with different brightness (Figure 4). The formula for CV is defined as follows: Where Sa and ma are the standard deviation and mean, respectively. Therefore, high, low, and intermediate CV values In order to better identify the edges, the mean of the image is added to the local mean.
where M is the mean of the image. In order to better identify the edges, the mean of the image is added to the local mean.

Difference of variances
where M is the mean of the image.

Difference of variances
The difference of variances (DoV) is the difference between the noise variance estimation and standard deviation of the local window, so homogeneous regions close to zero and edge regions have greater values.
where std (x) and estimate_noise (X) are the standard deviation of the local window (x) and the noise variance estimation of image (X), respectively. Its window size is w = (5 × 5). Figure 5 shows the outcome of DoV w=5 in different speckle noise. As can be seen, DoV 5 is stable during changes in noise intensity.
Remote Sens. 2020, 12, 2371 8 of 32 The difference of variances (DoV) is the difference between the noise variance estimation and standard deviation of the local window, so homogeneous regions close to zero and edge regions have greater values. DoVw = (std(x) -estimate_noise(X)) (18) where std (x) and estimate_noise (X) are the standard deviation of the local window (x) and the noise variance estimation of image (X), respectively. Its window size is w = (5 × 5). Figure 5 shows the outcome of DoVw=5 in different speckle noise. As can be seen, DoV5 is stable during changes in noise intensity.

The Proposed Extended Guided Filter
We define the proposed edge-aware weighting (PEAW) s as follows: where K is a constant obtained experimentally and S is combined into the cost function E(ak, bk). The criterion of a "homogeneous area" or an "edge area" is determined by the parameter , and the areas with variance (σ2) < are smoothed, whilst the areas with variance (σ2) > are preserved. Therefore, by replacing ε with in Equation (6) it is possible to maintain the edge more efficiently. In addition, the window size of DoV is 5 and if w becomes greater than 5, the edges of the DoV image become blurry and the guide filter cannot smooth the homogeneous areas around the edges properly. As mentioned, an EGF minimizes the output qi and the input pi. Equation (20) shows a cost function with applied PEAW.
The optimal value of and the optimal value are calculated as: Finally, is defined as follows: where is the mean values of and is ℎ within the window, respectively. Figure 6 shows the effect of a guide filter with DoV and without DoV on a Lena image.

The Proposed Extended Guided Filter
We define the proposed edge-aware weighting (PEAW) s as follows: where K is a constant obtained experimentally and S is combined into the cost function E(ak, bk). The criterion of a "homogeneous area" or an "edge area" is determined by the parameter ε, and the areas with variance (σ2) < ε are smoothed, whilst the areas with variance (σ2) > ε are preserved. Therefore, by replacing ε with ε s in Equation (6) it is possible to maintain the edge more efficiently. In addition, the window size of DoV is 5 and if w becomes greater than 5, the edges of the DoV image become blurry and the guide filter cannot smooth the homogeneous areas around the edges properly. As mentioned, an EGF minimizes the output qi and the input pi. Equation (20) shows a cost function with applied PEAW.
The optimal value of a k and the optimal value b k are calculated as: Finally,q i is defined as follows:q whereb k is the mean values of b k andâ k is the mean values o f a k within the window, respectively. Figure 6 shows the effect of a guide filter with DoV and without DoV on a Lena image.

Experimental Results
All the experimental outcomes are assessed in MATLAB = R2018b on Intel(R) Core(TM) i5-8500 CPU M 430 @ 3.0 GHz, 16 GB RAM and 64-bit operating system. Table 1 presents the simulation conditions for the proposed method. Table 1. Present the simulation conditions for the proposed method.

EAWF EGF EGF WLS Filter
Window size = (3 × 3) 2 guided by outcome of EAWF NeighborhoodSize = 7 DegreeOfSmoothing = 0.01 × diff(getrangefromclass(I)) 2 guided by outcome of EAWF During the experimental work, simulation SAR images, real SAR images, and standard optical images impressed with speckles are used. In the simulation SAR outcomes, the presence of the speckle is already there in the reference SAR image, so the real effectiveness and strength of despeckling scheme is checked by experimenting with the proposed method in 14 standard optical images (i.e., 'Lena', 'Boat',…) in speckle adding experiments instead of using SAR images that have already been impressed with speckle noise.
In the beginning, we used six standard images and the original images are shown in Figure 7. Speckle noise is added for speckle noise removal at noise (σ = 0.04 and number of looks L = 25)

Experimental Results
All the experimental outcomes are assessed in MATLAB = R2018b on Intel(R) Core(TM) i5-8500 CPU M 430 @ 3.0 GHz, 16 GB RAM and 64-bit operating system. Table 1 presents the simulation conditions for the proposed method. Table 1. Present the simulation conditions for the proposed method. 2 guided by outcome of EAWF 2 guided by outcome of EAWF

EAWF EGF EGF WLS Filter
During the experimental work, simulation SAR images, real SAR images, and standard optical images impressed with speckles are used. In the simulation SAR outcomes, the presence of the speckle is already there in the reference SAR image, so the real effectiveness and strength of despeckling scheme is checked by experimenting with the proposed method in 14 standard optical images (i.e., 'Lena', 'Boat', . . . ) in speckle adding experiments instead of using SAR images that have already been impressed with speckle noise.
In the beginning, we used six standard images and the original images are shown in Figure 7. Speckle noise is added for speckle noise removal at noise (σ = 0.04 and number of looks L = 25).
Remote Sens. 2020, 12, x FOR PEER REVIEW 9 of 42 First, the EAWF was applied to the input image. Figure 8a-f shows three noisy images and EAWF outcomes. Then, a logarithmic transformation was applied to the resulting EAWF image in order to convert multiplicative noise into additive noise. Next, to remove the additive noise and preserve edge information, EGF was used. Figure 8j-l shows the application of EGF for the first time with s = K × DoV, K = 150, where the filtering process is guided by image G which is the outcome of EAWF. As can be seen in Figure 8j-l, after applying the EGF on the image, some spots appear on homogeneous areas, which can be reduced by re-applying the EGF with different windows. The use of CV will be useful for softening the areas with high homogeneity (Figure 8m-o). In order to avoid over-softening, the parameters of this filter are also considered to be in small amounts. In addition, if the WLS filter is applied, after the first use of EGF, adjusting the WLS filter parameters leads to the removal of image details to achieve the desired ENL. Therefore, the EGF is applied to the image for the second time with s = K × CV', K = 4 ( Figure 8p-r), where the filtering process is guided by image G which is the outcome of the EAWF. Finally, in order to achieve the desired ENL, WLS Filter is applied to a homogenous region of the image (Figure 8s-u). Equation (24)(25)(26) shows the steps of applying the WLS filter to homogeneous regions.
Edge region = CV' Denoised image = WLS (I× (1-CV')) + I × (CV') (26) where I is the result of the EGF despeckling.  First, the EAWF was applied to the input image. Figure 8a-f shows three noisy images and EAWF outcomes. Then, a logarithmic transformation was applied to the resulting EAWF image in order to convert multiplicative noise into additive noise. Next, to remove the additive noise and preserve edge information, EGF was used. Figure 8j-l shows the application of EGF for the first time with s = K × DoV, K = 150, where the filtering process is guided by image G which is the outcome of EAWF. As can be seen in Figure 8j-l, after applying the EGF on the image, some spots appear on homogeneous areas, which can be reduced by re-applying the EGF with different windows. The use of CV will be useful for softening the areas with high homogeneity (Figure 8m-o). In order to avoid over-softening, the parameters of this filter are also considered to be in small amounts. In addition, if the WLS filter is applied, after the first use of EGF, adjusting the WLS filter parameters leads to the removal of image details to achieve the desired ENL. Therefore, the EGF is applied to the image for the second time with s = K × CV , K = 4 (Figure 8p-r), where the filtering process is guided by image G which is the outcome of the EAWF. Finally, in order to achieve the desired ENL, WLS Filter is applied to a homogenous region of the image (Figure 8s where I is the result of the EGF despeckling. To mention the advantages of EAWF and EGF in the proposed method, we studied the performance of the sub-filters of the proposed method. The denoising result of EAWF+EGF+WLS, EGF+WLS, and EAWF+WLS are shown step by step in Table 2 to verify the correctness and necessity of the designed components in the proposed method. Tables 2 shows ENL, PSNR (dB), STD, and SSIM values of the despeckled standard images using the sub-filters of the proposed method. The ENL measures the degree of speckle reduction in a homogenous area. Generally, a higher ENL value corresponds to better speckle elimination but a large STD corresponds to higher speckle noise To mention the advantages of EAWF and EGF in the proposed method, we studied the performance of the sub-filters of the proposed method. The denoising result of EAWF+ EGF+WLS, EGF+ WLS, and EAWF+ WLS are shown step by step in Table 2 to verify the correctness and necessity of the designed components in the proposed method. Table 2 shows ENL, PSNR (dB), STD, and SSIM values of the despeckled standard images using the sub-filters of the proposed method. The ENL measures the degree of speckle reduction in a homogenous area. Generally, a higher ENL value corresponds to better speckle elimination but a large STD corresponds to higher speckle noise According to Table 2, the denoising performance of EGF+WLS filter is reduced for the monarch image (PSNR = 25.86506 (−12.67%), SSIM = 25.86 (−21.57%), ENL = 230.84 (−90.34%) and STD = 0.030 (−64.44%)). In other images, the conditions are the same. The mean of the decline rate in EGF+WLS filter is reduced (PSNR = −12.53%, SSIM = −24.15%, ENL = −88.83% and STD = −66.25%). Therefore, the use of EAWF can increase PSNR by 12.53%, SSIM by 24.15%, ENL by 88.83% and STD by −66.25%. On the other hand, the use of EGF can increase PSNR by 3.32%, SSIM by 10.06%, ENL by 82.73% and STD by −58.80%. As can be seen from the mean of the decline rate in Table 2, the EAWF+ WLS filter has a better performance compared to the EGF + WLS filter. Thus, the EAWF is more efficient than EGF. Since EAWF+ EGF+ WLS has the best performance, the combination of these filters is synergistic and compensates for individual weaknesses. When considering the EAWF + EGF + WLS, the PSNR value may be slightly reduced by adding filters (Monarch, Man, Boat, Peppers, and Cameraman). This decrease is less than 2%, but the ENL value is increased by adding filters for all images. This increase is between 41% and 329% for the monarch image, between 22% and 476% for the man image, between 40% and 318% for the Boat image, between 29% and 647% for the Lena image, between 14% and 340% for the Peppers image, and between 13% and 506% for the Cameraman image. In addition, the STD value is improved similarly to ENL but the SSIM changes are minor.
Remote Sens. 2020, 12, x; doi: FOR PEER REVIEW www.mdpi.com/journal/remotesensing According to Table 2, the denoising performance of EGF+WLS filter is reduced for the monarch image (PSNR = 25.86506 (-12.67%), SSIM = 25.86 (-21.57%), ENL = 230.84 (-90.34%) and STD = 0.030 (-64.44%)). In other images, the conditions are the same. The mean of the decline rate in EGF+WLS filter is reduced (PSNR = -12.53%, SSIM = -24.15%, ENL = -88.83% and STD = -66.25%). Therefore, the use of EAWF can increase PSNR by 12.53%, SSIM by 24.15%, ENL by 88.83% and STD by -66.25%. On the other hand, the use of EGF can increase PSNR by 3.32%, SSIM by 10.06%, ENL by 82.73% and STD by -58.80%. As can be seen from the mean of the decline rate in Table 2, the EAWF+ WLS filter has a better performance compared to the EGF + WLS filter. Thus, the EAWF is more efficient than EGF. Since EAWF+ EGF+ WLS has the best performance, the combination of these filters is synergistic and compensates for individual weaknesses. When considering the EAWF + EGF + WLS, the PSNR value may be slightly reduced by adding filters (Monarch, Man, Boat, Peppers, and Cameraman). This decrease is less than 2%, but the ENL value is increased by adding filters for all images. This increase is between 41% and 329% for the monarch image, between 22% and 476% for the man image, between 40% and 318% for the Boat image, between 29% and 647% for the Lena image, between 14% and 340% for the Peppers image, and between 13% and 506% for the Cameraman image. In addition, the STD value is improved similarly to ENL but the SSIM changes are minor.
In the next comparison, we used 14 standard images. The original images are shown in Figure 9. Speckle noise is added for speckle noise removal at noise (σ = 0.04 and number of looks L = 25). The standard methods used for comparison between different filters are SAR-BM3D [28], NLM [29], WLS [30], bitonic [31], guided [32], Lee [33], Frost [34], anisotropic diffusion filter with memory based on speckle statistics (ADMSS) [35], non-local low-rank (NLLR) [36], SRAD-guided [37], SRAD [38], and Choi et al. [1]. Table 3 illustrates the optimal parameters of existing filters.  Table 3. The optimal parameters of existing filters in standard images.   Table 3. The optimal parameters of existing filters in standard images.  The SSIM values of the proposed and the standard methods are shown in Table 5. As can be seen, the SRAD filter provides the best edge preservation performance in Baboon  Table 6 shows the number of the best, the second best, and the sum of both. As shown in Table 6, the performance of the proposed method is better than other methods. Figure  The SSIM values of the proposed and the standard methods are shown in Table 5. As can be seen, the SRAD filter provides the best edge preservation performance in Baboon = 0.65 and Hill= 0.73 and the proposed method of Choi Table 6 shows the number of the best, the second best, and the sum of both. As shown in Table 6, the performance of the proposed method is better than other methods. Figure  In Figure 10b-e and 10g-i, the noise of speckle residue is represented in homogeneous areas. Speckle noise reduction performance of the SRAD-guided and the WLS methods are better than the GF, Frost, Lee, Bitonic, NLLR, ADMSS, and SRAD methods, as these methods show a blurring in the image. The visual quality and edge reservation performance of the method proposed by Choi et al. and SAR-BM3D filters are also excellent, but these filters show artifacts in the homogeneous area (Figure 10k-l). As can be seen, the proposed method exhibits robust denoising and edge preservation abilities. In Figure 10b-e and 10g-i, the noise of speckle residue is represented in homogeneous areas. Speckle noise reduction performance of the SRAD-guided and the WLS methods are better than the GF, Frost, Lee, Bitonic, NLLR, ADMSS, and SRAD methods, as these methods show a blurring in the image. The visual quality and edge reservation performance of the method proposed by Choi et al. and SAR-BM3D filters are also excellent, but these filters show artifacts in the homogeneous area (Figure 10k-l). As can be seen, the proposed method exhibits robust denoising and edge preservation abilities.

Experiments on Real SAR Images
To consider the actual performance of the proposed filter, we examined the proposed filter in the real SAR image. In this section, three SAR images are described (Figures 11-13). The actual SAR image depicts a rural scene (512 × 512) [39], capitol building scene (1232 × 803), and an image of a C-130s on a flight line (600 × 418) [40]. Table 7 shows that the proposed method has the best performance in terms of ENL. The WLS filter also has the second rank in speckle noise suppression performance. For SAR images, the level of noise is related to L. When the look number is not known, finding the mean of several ENL is a common way to obtain the L [41]. According to Table 7, the estimated look number is L = 15.
Remote Sens. 2020, 12, x; doi: FOR PEER REVIEW www.mdpi.com/journal/remotesensing Figure 11 shows the outcomes of despeckled filters, demonstrating that some methods, like guided, Frost, Lee, bitonic, NLLR, and SRAD, do not have a strong robust denoising ability (Figure 11b-e,g,i). Table  7 shows that the proposed method demonstrates the best ENL value and WLS exhibits second-best ENL value, but it shows a blurring phenomenon (Figure 11f). Compared with SAR-BM3D and Choi et al. proposed method, the SAR-guided method exhibits lower edge preservation and denoising performances. The SAR-BM3D and Choi et al. methods have good edge preservation and despeckling performance; meanwhile, artifacts in the homogeneous areas are noticeable (Figure 11k). A comparison of the proposed method with Choi et al. and SAR-BM3D filters shows that the proposed method has a better edge preservation performance (Figure 11m). In the following, another real SAR image is evaluated by ENL and STD ( Figure 12, Table 8). Generally, a large STD corresponds to higher speckle noise. The standard methods used for comparison are GF, SAR-BM3D, Bilateral filter, Fast Bilateral filter, WLS, DPAD, DPAD, and the proposed method of Fang et al. [42]. Table 9 presents the parameters of different filters. Remote Sens. 2020, 12, x; doi: FOR PEER REVIEW www.mdpi.com/journal/remotesensing simulated SAR image is evaluated by PSNR, SNR, SSIM, and MAE (Table 10). Figure 13 shows the original SAR image and the noisy image, respectively, whose number of looks L=25, 16, 12, and 10, and the variance of the noise, were 0.04, 0.06, 0.08, and 0.1. The purpose of showing the outcome in the simulated SAR image is to test the validity, robustness, effectiveness, and adaptive features of the despeckling method at diverse noise variances. The despeckling is applied to a speckled SAR image (600 × 418) to validate the efficiency of the proposed method.   Figure 11 shows the outcomes of despeckled filters, demonstrating that some methods, like guided, Frost, Lee, bitonic, NLLR, and SRAD, do not have a strong robust denoising ability (Figure 11b-e,g,i). Table 7 shows that the proposed method demonstrates the best ENL value and WLS exhibits second-best ENL value, but it shows a blurring phenomenon (Figure 11f). Compared with SAR-BM3D and Choi et al. proposed method, the SAR-guided method exhibits lower edge preservation and denoising performances. The SAR-BM3D and Choi et al. methods have good edge preservation and despeckling performance; meanwhile, artifacts in the homogeneous areas are noticeable (Figure 11k). A comparison of the proposed method with Choi et al. and SAR-BM3D filters shows that the proposed method has a better edge preservation performance (Figure 11m).
In the following, another real SAR image is evaluated by ENL and STD ( Figure 12, Table 8). Generally, a large STD corresponds to higher speckle noise. The standard methods used for comparison are GF, SAR-BM3D, Bilateral filter, Fast Bilateral filter, WLS, DPAD, DPAD, and the proposed method of Fang et al. [42]. Table 9 presents the parameters of different filters. Figure 12 exhibits that bilateral filter does not show strong despeckling ability (Figure 12e). The WLS and fast bilateral filter show a blurring phenomenon in the despeckled image (Figure 12d-f). Based on Table 8, the proposed method represents the second-best ENL and STD values. However, it exhibits excellent performance in edge preservation abilities (Figure 12g). According to Table 8, the estimated look number is 23. Table 8 shows that the filter SAR-BM3D has a good performance but, as can be seen in Figure 12-region1 and Figure 12-region 2, sharp changes in the homogeneous area lead to artifacts in the homogeneous areas. Table 8 shows that WLS represents the best ENL and STD values. In order to compare the proposed method and WLS filter, we examined the pixel changes of these two filters and the real SAR image. WLS filter shows a smoothing at the edge area ( Figure 12-region 3 and Figure 12-region 4) but the proposed method can preserve the edges of the image.  Table 9. The parameters of different filters used in this comparison. In the simulated SAR image experiment, the generation of speckle noise is performed through modeling of the multiplicative speckle noise using Equation (14). The noise distribution in the actual SAR images is unknown. Therefore, the actual SAR images are not possible to test the algorithm at different noise variances. For this purpose, the concept of simulated SAR images is introduced [43]. Furthermore, a simulated SAR image is evaluated by PSNR, SNR, SSIM, and MAE (Table 10). Figure 13 shows the original SAR image and the noisy image, respectively, whose number of looks L=25, 16, 12, and 10, and the variance of the noise, were 0.04, 0.06, 0.08, and 0.1. The purpose of showing the outcome in the simulated SAR image is to test the validity, robustness, effectiveness, and adaptive features of the despeckling method at diverse noise variances. The despeckling is applied to a speckled SAR image (600 × 418) to validate the efficiency of the proposed method. According to Table 10, the proposed method achieved the best results in the three evaluation indexes of SNR, PSNR, and MAE when noise variance is 0.06, 0.08, and 0.1. Table 10 shows that the proposed method represents the second-best SSIM values when noise variance is 0.04 and 0.08. This means that this algorithm showed satisfactory results. Generally, the proposed method can preserve the edges of the image, suppress the noise effectively, and retain the edge details to some extent.

Computational Complexity
The time consumption of the proposed and the standard methods for 17 images are shown in Tables 11-18. According to Tables 11-13, the proposed method is faster

Discussion
This study used the EAWF, EGF, and WLS filters for the despeckling of SAR images. The most conventional methods are developed for additive white Gaussian noise. Therefore, additive noise in sensing systems and imaging is common. Since speckle noise is a multiplicative noise, EAWF is employed to reduce noise levels and increase PNSR.
During the experimental work, the simulation SAR images, real SAR images, and standard optical images impressed with speckles are used. To consider the actual performance of the proposed filter, we examined the proposed filter in the real SAR image. The purpose of using the simulated SAR image is to test the validity, robustness, effectiveness, and adaptive feature of the despeckling method at diverse noise variances. In the simulation SAR outcomes, the presence of the speckle is already there in the reference SAR image, so the real effectiveness and strength of the despeckling scheme are checked by standard optical images impressed with speckles. According to Table 2, the use of EAWF can increase PSNR by 12.53%, SSIM by 24.15%, ENL by 88.83%, and STD by −66.25%. On the other hand, the use of EGF can increase PSNR by 3.32%, SSIM by 10.06%, ENL by 82.73%, and STD by −58.80%. Thus, the EAWF is more efficient than EGF. Since EAWF + EGF + WLS has the best performance, the combination of these filters is synergistic. When considering EAWF + EGF + WLS, the increase in PSNR value may be slight (about 2%), but the ENL value is increased between 41% and 329% for the Monarch image, between 22% and 476% for the Man image, between 40% and 318% for the Boat image, between 29% and 647% for the Lena image, between 14% and 340% for the Peppers image, and between 13% and 506% for Cameraman image.
The EGF shows excellent noise removal and edge preservation. As can be seen in Figure 6, the new edge-aware EGF filter is better than classic GF. According to Table 7, the WLS filter exhibits the best ENL value (between all filters except the proposed method) and edge preservation performance. Therefore, we adopted the WLS method to increase ENL. As shown in Tables 4-6, the proposed method has the best outcome in PNSR (5 best and 7 second best-the PSNR values of the proposed method exhibit the best performance of de-speckling in the images (Boat = 28.24 dB; Cameraman = 28.43 dB; Fruits = 27.79 dB; Napoli = 26.83 dB and Peppers = 28.53 dB)) and SSIM (9 best and 4 second best-the proposed method exhibits the best edge preservation performance in Airplane = 0.84, Boat = 0.79; Cameraman = 0.82; Fruits = 0.78, Lena = 0.85; Man = 0.78; Monarch = 0.90; Napoli = 0.80; and Peppers = 0.85). In SAR image 1, the proposed method demonstrates the best ENL value in Table 7. In SAR image 2, the proposed method has second-best ENL and STD values in Table 8. In SAR image 3, according to Table 10, the proposed method achieved the best results in the three evaluation indexes of SNR, PSNR, and MAE, when the noise variance is 0.06, 0.08, and 0.1. It also shows that the proposed method represents the second-best SSIM values when noise variance is 0.04 and 0.08. According to Tables 11-16

Conclusions
We propose a hybrid filter based on EAWF, EGF, and WLS Filter to remove the speckle noise. For this purpose, the EAWF method was used as a preprocessing filter. EAWF is applied to the SAR image, directly. After that, the logarithmic transform was applied to create additive noise from the multiplicative noise. We also developed GF based on new edge-aware weighting. The proposed EGF can remove the additive noise and preserve the edge information more efficiently than GF. After applying the EGF to the image, some spots appear in homogeneous areas, which can be reduced by re-applying the EGF with different windows. Finally, in order to achieve the desired ENL, the WLS Filter is applied to a homogenous region of the image. For better evaluation, we used the simulation SAR images, real SAR images, and standard optical images with speckle noise. The experimental outcome shows that the proposed method has the best despeckling and edge preservation and has an acceptable runtime as well.