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

Abstract

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 efficiently 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 different 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.

1. 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, Frost filtering [2] and Lee filtering [3]. However, the spatial methods tend to darken the despeckled SAR images. In recent years, model-based filters are being used for SAR image despeckling [4] such as the block sorting for the SAR image denoising algorithm [5]. These filters are useful for solving different inverse problems but they are often time-consuming. Lately, scientists have presented many image fusion methods, the two known image fusion filters among which are Multi-scale image fusion filters and data-driven image fusion filters [6]. However, these Filters do not fully consider spatial consistency and tend to produce color distortion and brightness.

Other popular filters include the partial differential equation (PDE), nonlinear, linear, multiresolution, hybrid, and denoising filters based on fuzzy logic.

The linear types of filtering are performed through a procedure known as convolution. The filters are obtained by the weighted sum of the neighbor pixels of the mask window. For example, the Gaussian and mean methods belong to linear filters. Due to its inability to detect image areas (edge, homogeneous, and details), the mean filter shows a low-edge preservation performance [7]. However, the Gaussian method shows good performance in small variance and the blurring phenomenon occurs within the edge areas.

In the nonlinear method, the output is not a linear function of its input (e.g., median filter, bilateral filter (BF) [8], non-local mean (NLM) filters [9], Weibull multiplicative model, etc). The median filter is similar to the mean filter representation of good performance and weak performance in homogenous regions and edge preservation, respectively. The BF and NLM filters have good performance in edge preservation, but in Rayleigh distribution of noise (speckle noise), the denoising performance is poor. In addition, BF represents gradient distortion and high complexity [10]. Moreover, Anantrasirichai [11] suggested an adaptive bilateral filter (ABF) for the imaging of optical coherence tomography. The range parameter is determined by the variance of the most homogeneous block, and it is automatically adapted based on speckle noise variations. But, given the sensitivity of variance to noise, the variance cannot correctly identify the homogeneous image in high noise. The NLM filter functions based on BF that is appropriate to additive white gaussian noise (AWGN) denoising, not despeckling [12]. Another popular model is the Weibull distribution but it is appropriate for urban scenes and sea clutter [13].

The PDE methods are useful to eliminate noise. In order to obtain a noise-free image, a noisy image is transformed into PDE forms [14]. Some filtering methods such as the adaptive window diffusion (AWAD) [15] are based on PDE, which is able to control the mask size and direction and shows good performance in edge preservation. However, the AWAD method that is based on a new diffusion function does not perform speckle denoising in homogeneous regions, so it has a low de-speckle performance.

In the field of fuzzy noise removal, Cheng et al. [16] developed a denoising method of synthetic aperture radar images, which is based on fuzzy logic and estimates the fuzzy edges of each pixel in the filter window and uses these to weigh the contributions of neighboring pixels to perform fuzzy filtering. Nonetheless, it is appropriate only for images with large homogenous regions, which is its main drawback. In addition, Babu et al. [17] proposed adaptive despeckling based on fuzzy logic for the classification of image regions. Then, the most appropriate filter was selected for the particular image region used only averaging and median filters, though.

The transform domain filters are mostly based on multi-resolution transforms such as Shearlet-domain SAR image denoising [18] and wavelet-domain [19]. Because multiresolution filters are able to eliminate noise at different frequencies, they are employed for despeckling. However, because of some inherent flaws, the transform domain methods cause pixel distortion, so hybrid filters have become more popular. Zhang and Gunturk [10] stated that noise may exist in the detailed and approximate sub-bands of images in the wavelet transform, so for speckle noise removal, different filters can be applied to individual sub-bands. Loganayagi et al. [20] proposed a robust denoising method based on BF. In addition, Kumar et al. proposed speckle denoising using tetrolet wavelets [21]. Since the BF is a single resolution, not all frequency components of the image are available. Accordingly, the wavelet filter is used to form a scale-space for the noisy image. The wavelet filter decomposition is able to distinguish signal from noise at various scales [22]. Mehta proposed a method that exploits the wavelet filter features with the estimation ability of the Wiener filter. To achieve better performance, they used the adaptive Wiener filter (AWF) to denoise the components of the wavelet sub-bands. Zhang proposed ultrasound image denoising using a combination of bilateral filtering and stationary wavelet [23]. Speckle noise in the low-pass approximation and high-pass detail are filtered by the fast bilateral filter and wavelet thresholding, respectively. Sari et al. proposed a denoising method through the subsequent application of bilateral filters and wavelet thresholding [24]. In these mentioned hybrid articles, wavelet decomposition is employed to divide the information of an image into approximation sub-band and detail sub-bands. A bilateral or Wiener filter is applied in different positions of the sub-bands. These algorithms show low speckle noise suppression ability due to the low ability to choose the optimal position and optimal parameters of filters. However, it is impossible to 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.

2. Materials and Methods

2.1. 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.

2.2. Adaptive Wiener Filter

One of the first methods developed for denoising in digital images is based on Wiener filtering. If we assume (n1, n2) is a particular pixel location, the AWF is given by [26].

$$AWF\left[I\left(n_1,n_2\right)\right]=\mu +\frac{{\sigma }^2-{\sigma }_n^2}{{\sigma }^2}\left(I\left(n_1,n_2\right)-\mu \right)$$

(1)

where I is the input image, variance (${\sigma }^2$) and mean µ are locally estimated from the set ℵ of (N × M) local neighborhood of each pixel. So that

$$\mu =\frac{1}{MN}{\displaystyle \sum }_{n_1,n_2ϵ\aleph }^{}I\left(n_1,n_2\right)$$

(2)

$${\sigma }^2=\frac{1}{MN}{\displaystyle \sum }_{n_1,n_2ϵ\aleph }^{}{I}^2\left(n_1,n_2\right)-{\mu }^2$$

(3)

In addition, (${\sigma }_n$) is the variance of the noise.

2.3. Guided Filter

GF transforms the output q_i for the guidance I_k.of the window ${\omega }_k$, and k is the center pixel in the window, as follows:

q_i = a_kI_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 ${\omega }_k$.

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:

$$E\left(a_k,b_k\right)={\displaystyle \sum }_{i\in {\omega }_k}^{}\left({\left(a_k{b}_k+b_k-p_i\right)}^2+\epsilon a_k^2\right)$$

(6)

where $\epsilon$ 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.

$$a_k=\frac{\frac{1}{\left|\omega \right|}{{\displaystyle \sum }}_{i\in {\omega }_k}^{}{I}_i{P}_i-{\mu }_k\underset{\_}{P_k}}{{\sigma }_k^2+ϵ}$$

(7)

$$b_k=\underset{\_}{P_k}-a_k{\mu }_k$$

(8)

where ${\sigma }_k^2$ and ${\mu }_k$ are the variance and the mean of the guidance image in the window ${\omega }_k$ and $\left|\omega \right|$ indicates the number of pixels in ${\omega }_k$, and $\underset{\_}{P_k}$=$\frac{1}{\left|\omega \right|}{P}_i$. As $\epsilon$ and the window size ${\omega }_k$ adjustment, the noise is deleted and the edge regions are preserved.

3. Proposed Algorithm

3.1. 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.

$$DI=\frac{{\sigma }^2}{\mu }$$

(9)

$$EAWF\left[I\left(n_1,n_2\right)\right]=\mu +\frac{DI-{\sigma }_n^2}{DI}\left(I\left(n_1,n_2\right)-\mu \right)$$

(10)

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).

$$\begin{array}{ll}EAWF\left[I\left(n_1,n_2\right)\right]& =\mu +\left(I\left(n_1,n_2\right)-\mu \right)-\frac{{\sigma }_n^2}{DI}\left(I\left(n_1,n_2\right)-\mu \right)=I\left(n_1,n_2\right)-\frac{{\sigma }_n^2}{DI}\left(I\left(n_1,n_2\right)-\mu \right)\\ & =I\left(n_1,n_2\right)-\mu \left(\frac{{\sigma }_n^2}{{\sigma }_{}^2}\left(I\left(n_1,n_2\right)-\mu \right)\right)\end{array}$$

(11)

In fact, $\frac{{\sigma }_n^2}{{\sigma }_{}^2}\left(I\left(n_1,n_2\right)-\mu \right)$ 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 $\frac{{\sigma }_n^2}{{\sigma }^2}\left(I\left(n_1,n_2\right)-\mu \right)$, a better approximation of noise is obtained ($\mu \left(\frac{{\sigma }_n^2}{{\sigma }_{}^2}\left(I\left(n_1,n_2\right)-\mu \right)\right)$). 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.

3.2. SAR Speckle Noise Model and Logarithmic Transformation

The following model is appropriate for images with multiplicative noise:

f(x,y) = g(x,y).ƞm(x,y) + ƞa(x,y)

(12)

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).ƞm(x,y)

(13)

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). ƞm(x,y) also defines the speckle due to fading. g(x,y) and ƞm(x,y) are independent. ƞm(x,y) conforms to a Gamma distribution where the variance is $\frac{1}{L}$ and the mean is one.

$${\rho }_{\mathrm{N}}(\mathrm{N})=\frac{L^L\mathsf{\eta }{m}^{L-1}EXP\left(-\mathsf{\eta }mL\right)}{\Gamma \left(L\right)}$$

(14)

where N $\ge$ 0, L $\ge$ 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)

(15)

3.3. Extended Guided Filter

3.3.1. A New Edge-Aware Weighting

1.

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:

$$CV=\frac{S_{\alpha }}{m_{\alpha }}\times 100\%$$

(16)

Where Sa and ma are the standard deviation and mean, respectively. Therefore, high, low, and intermediate CV values correspond to ‘edges’, ‘homogenous’, and ‘detail’.

In order to better identify the edges, the mean of the image is added to the local mean.

$$CV\prime =\frac{S_{\alpha }}{m_{\alpha }+M}\times 100\%$$

(17)

where M is the mean of the image.

2.

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.

DoV_w = (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 DoV_w=5 in different speckle noise. As can be seen, DoV₅ is stable during changes in noise intensity.

3.3.2. The Proposed Extended Guided Filter

We define the proposed edge-aware weighting (PEAW) s as follows:

S = K × DOV_w=5

(19)

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 $\epsilon ,$ and the areas with variance (σ2) < $\epsilon$ are smoothed, whilst the areas with variance (σ2) > $\epsilon$ are preserved. Therefore, by replacing ε with $\frac{\epsilon }{s}$ 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.

$$E\left(a_{k\prime },b_{k\prime }\right)={\displaystyle \sum }_{i\in {\omega }_{k\prime }}^{}\left({\left(a_{k\prime }{b}_{k\prime }+b_{k\prime }-p_i\right)}^2+\frac{\epsilon }{s}{a}_{k\prime }^2\right)$$

(20)

The optimal value of $a_{k\prime }$ and the optimal value $b_{k\prime }$ are calculated as:

$$a_{k\prime }=\frac{\frac{1}{\left|\omega \right|}{{\displaystyle \sum }}_{i\in {\omega }_k\prime }^{}{I}_i{P}_i-{\mu }_{k\prime }\underset{\_}{P_{k\prime }}}{{\sigma }_{k\prime }^2+\frac{ϵ}{s}}$$

(21)

$$b_{k\prime }=\underset{\_}{P_{k\prime }}-a_{k\prime }{\mu }_{k\prime }$$

(22)

Finally, $\widehat{q_i}$ is defined as follows:

$$\widehat{q_i}=\widehat{a_k}{I}_k+\widehat{b_k}$$

(23)

where $\widehat{b_k}$ is the mean values of $b_{k\prime }$ and $\widehat{a_k}$ is $themeanvaluesof{a}_{k\prime }$ within the window, respectively. Figure 6 shows the effect of a guide filter with DoV and without DoV on a Lena image.

4. 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. Present the simulation conditions for the proposed method.

EAWF	EGF	EGF	WLS Filter
Window size = (3 × 3)	NeighborhoodSize = 8 DegreeOfSmoothing = 0.2 × diff(getrangefromclass(I))2 guided by outcome of EAWF	NeighborhoodSize = 7 DegreeOfSmoothing = 0.01 × diff(getrangefromclass(I))2 guided by outcome of EAWF	Lambda = 0.1 Alpha = 1

presents the simulation conditions for the proposed method.

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).

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 (24–26) shows the steps of applying the WLS filter to homogeneous regions.

Homogenous region = (1-CV’)

(24)

Edge region = CV’

(25)

Denoised image = WLS (I× (1-CV’)) + I × (CV’)

(26)

where I is the result of the EGF despeckling. Figure 8s–u shows the final outcome of image 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. The sub-filters performance of the proposed method.

			EAWF + EGF + WLS				EGF + WLS				EAWF + WLS
	Noise Variance	Filters	PSNR	SSIM	ENL	STD	PSNR	SSIM	ENL	STD	PSNR	SSIM	ENL	STD
	0.04	Noisy image	21.117	0.3442	24.406	0.0943	21.1173	0.34425	24.405	0.0943	21.117	0.3442	24.406	0.0943
		EAWF	28.013	0.7221	191.53	0.0336	-	-	-	-	27.986	0.7203	183.34	0.0345
		EAWF+EGF	29.736	0.8675	821.3	0.0161	22.4528	0.39538	37.332	0.0758	-	-	-	-
		EAWF+2(EGF)	29.813	0.8953	1683.6	0.0113	23.8474	0.50649	75.113	0.0531	-	-	-	-
		EAWF+2(EGF)+WLS	29.618	0.8958	2388.9	0.0095	25.8651	0.70259	230.84	0.0301	29.265	0.8338	429.12	0.0225
		The rate of decline	-	-	-	-	-12.67%	-21.57%	-90.34%	-68.44%	-1.19%	-6.92%	-82.04%	-57.78%
Man (512 × 512)	0.04	Noisy image	21.67	0.5741	25.194	0.1226	21.67	0.5741	25.194	0.1226	21.67	0.5741	25.194	0.1226
		EAWF	27.953	0.7722	161.71	0.0485	-	-	-	-	27.953	0.7722	161.71	0.0485
		EAWF+EGF	28.93	0.8198	928.79	0.0202	23.8873	0.62597	60.549	0.0779	-	-	-	-
		EAWF+2(EGF)	28.65	0.809	1463.4	0.0161	24.6302	0.64974	96.923	0.0614	-	-	-	-
		EAWF+2(EGF)+WLS	28.044	0.782	1798.2	0.0145	26.5694	0.73599	221.2	0.0405	28.506	0.795	293.84	0.0357
		The rate of decline	-	-	-	-	-5.26%	-5.89%	-87.70%	-64.20%	1.65%	1.66%	-83.66%	-59.38%
Boat (512 × 512)	0.04	Noisy image	18.892	0.3536	24.894	0.1256	18.8922	0.35363	24.894	0.1256	18.892	0.3536	24.894	0.1256
		EAWF	26.014	0.6072	162.64	0.0492	-	-	-	-	26.014	0.6072	162.64	0.0492
		EAWF + EGF	28.21	0.7562	678.86	0.024	20.8253	0.38558	59.827	0.07980	-	-	-	-
		EAWF + 2(EGF)	28.414	0.7902	1344.5	0.0171	21.4729	0.40022	95.768	0.06290	-	-	-	-
		EAWF + 2(EGF) + WLS	28.283	0.7927	1883.5	0.0144	23.1636	0.45335	218.56	0.04149	27.14	0.6697	324.69	0.0348
		The rate of decline	-	-	-	-	-18.10%	-42.81%	-88.40%	-65.29%	-4.04%	-15.51%	-82.76%	-58.62%
Lena (512 × 512)	0.04	Noisy image	19.8	0.3978	24.038	0.1333	19.7995	0.39779	24.037	0.1333	19.8	0.3978	24.038	0.1333
		EAWF	26.873	0.6713	171.85	0.0499					26.873	0.6713	171.85	0.0499
		EAWF + EGF	28.951	0.8497	1279.7	0.0182	22.4346	0.46393	49.816	0.0923
		EAWF + 2(EGF)	29.748	0.8576	2240.6	0.0138	23.7064	0.52094	87.360	0.0693
		EAWF + 2(EGF) + WLS	30.137	0.8504	2907.6	0.0121	25.7009	0.65416	203.84	0.0452	27.914	0.7469	312.74	0.0371
		The rate of decline	-	-	-	-	-14.72%	-23.07%	-92.99%	-73.23%	-7.38%	-12.16%	-89.24%	-67.39%
Peppers (512 × 512)	0.04	Noisy image	19.987	0.3539	24.356	0.1379	19.987	0.35385	24.355	0.1379	19.987	0.3539	24.356	0.1379
		EAWF	26.784	0.6106	127.21	0.0603	-	-	-	-	26.784	0.6106	127.21	0.0603
		EAWF + EGF	29.862	0.7598	559.2	0.0288	22.64196	0.430494	47.345	0.0984	-	-	-	-
		EAWF + 2(EGF)	29.965	0.7729	814.29	0.0238	23.7408	0.47675	69.794	0.0807	-	-	-	-
		EAWF + 2(EGF) + WLS	29.906	0.7742	930.47	0.0223	25.9545	0.60132	125.54	0.06	28.278	0.6835	169.52	0.0525
		The rate of decline	-	-	-	-	-13.21%	-22.33%	-86.51%	-62.83%	-5.44%	-11.71%	-81.78%	-57.52%
Cameraman (512 × 512)	0.04	Noisy image	19.64	0.3972	24.43	0.1313	19.6395	0.39716	24.430	0.1313	19.64	0.3972	24.43	0.1313
		EAWF	26.784	0.6273	165.07	0.0505	-	-	-	-	26.784	0.6273	165.07	0.0505
		EAWF + EGF	29.401	0.8302	836.91	0.0224	22.4336	0.45352	52.343	0.0888	-	-	-	-
		EAWF + 2(EGF)	29.351	0.8439	1126.1	0.0193	23.6573	0.49083	79.734	0.0717	-	-	-	-
		EAWF + 2(EGF) + WLS	29.121	0.8378	1279.7	0.0181	25.859	0.59268	165.47	0.0496	28.096	0.7062	295.53	0.0378
		The rate of decline	-	-	-	-	-11.20%	-29.25%	-87.07%	-63.51%	-3.52%	-15.70%	-76.91%	-52.12%
		Mean of decline rate	-	-	-	-	-12.53%	-24.15%	-88.83%	-66.25%	-3.32%	-10.06%	-82.73%	-58.80%

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.

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. The optimal parameters of existing filters in standard images.

Methods	Optimal Parameters
NLM	Mask size = 3 × 3
Frost	Mask size = 3 × 3
Lee	Mask size = 3 × 3
Bitonic	Mask size = 3 × 3
WLS	Mask size = 3 × 3, λ = 3
NLLR	Β = 10, H = 10
ADMSS	Δt = 0.5, $\sigma =\rho =0.1,n_{iter}=15$
SAR-BM3D	Number of rows/cols of block = 9, Maximum size of the 3rd dimension of a stack = 16, Diameter of search area = 39, Dimension of step = 3, Parameter of the 2D Kaiser window = 2, transform UDWT = daub4

illustrates the optimal parameters of existing filters.

Table 4. Peak signal-to-noise (PSNR) (in dB) results for each standard image (The best value is shown in bold and the second-best value is shown in red color).

	Noisy	NLM	Guided	Frost	Lee	Bitonic	WLS	NLLR	ADMSS	SRAD	SARD-Guided	SAR-BM3D	Choi at al	Proposed
Airplane	16.53	19.12	19.14	22.06	23.78	26.18	24.97	17.39	23.43	26.97	26.53	28.10	27.45	27.91
Baboon	18.49	21.13	21.09	21.08	21.91	21.97	21.97	19.53	18.28	23.52	22.07	22.51	22.92	23.08
Barbara	19.16	22.40	22.05	22.34	23.26	23.68	23.78	20.39	20.50	24.99	23.75	28.32	24.59	25.94
Boat	18.46	21.81	21.68	23.36	19.41	26.39	25.50	19.65	20.14	27.37	26.59	27.20	27.55	28.24
Camera-man	18.66	21.65	21.59	22.41	22.85	24.43	25.03	19.75	17.59	26.73	24.71	26.35	26.87	28.43
Fruits	17.08	19.96	19.98	22.30	24.08	26.33	26.31	18.04	22.07	27.45	26.93	27.68	27.45	27.79
Hill	19.79	23.54	23.38	24.64	25.48	27.58	26.75	21.26	24.92	28.25	27.82	28.30	28.27	28.19
House	17.93	21.16	21.02	23.26	25.06	27.38	25.93	19.09	22.46	27.58	27.81	29.83	28.58	28.90
Lena	18.84	22.45	22.31	24.29	25.88	28.54	27.39	20.11	21.88	29.69	28.99	29.91	30.13	28.38
Man	19.51	23.07	22.94	24.41	26.15	27.46	26.46	20.83	20.82	28.31	27.68	27.71	28.55	28.00
Monarch	20.19	24.55	24.10	25.11	26.76	27.70	25.87	21.99	24.00	29.50	28.03	29.54	29.64	29.59
Napoli	21.00	24.62	24.27	24.06	24.48	24.34	23.69	22.71	22.90	26.41	24.34	25.14	25.70	26.83
Peppers	18.74	22.05	21.79	23.50	22.92	26.62	25.77	19.96	18.13	28.29	27.22	27.13	28.44	28.53
Zelda	21.18	26.23	25.94	26.71	28.62	31.40	30.66	23.19	29.28	32.67	32.20	32.38	32.77	32.58

and

Table 5. Structural similarity (SSIM) results for each standard image (The best value is shown in bold and the second-best value is shown in red color).

	Noisy	NLM	Guided	Frost	Lee	Bitonic	WLS	NLLR	ADMSS	SRAD	SARD-Guided	SAR-BM3D	Choi at al	Proposed
Airplane	0.21	0.29	0.28	0.37	0.50	0.66	0.70	0.25	0.73	0.72	0.76	0.84	0.82	0.84
Baboon	0.49	0.56	0.56	0.47	0.54	0.52	0.53	0.53	0.39	0.65	0.53	0.56	0.61	0.57
Barbara	0.44	0.61	0.57	0.50	0.60	0.64	0.67	0.55	0.52	0.68	0.65	0.84	0.69	0.75
Boat	0.33	0.46	0.44	0.47	0.60	0.68	0.67	0.40	0.39	0.71	0.70	0.72	0.73	0.79
Camera-man	0.42	0.49	0.48	0.48	0.57	0.67	0.73	0.45	0.36	0.76	0.74	0.80	0.80	0.83
Fruits	0.18	0.28	0.27	0.33	0.48	0.64	0.70	0.23	0.43	0.76	0.76	0.78	0.78	0.78
Hill	0.38	0.56	0.54	0.53	0.64	0.69	0.68	0.49	0.58	0.73	0.71	0.73	0.73	0.72
House	0.25	0.41	0.38	0.41	0.53	0.67	0.71	0.33	0.53	0.78	0.76	0.84	0.78	0.81
Lena	0.29	0.45	0.43	0.45	0.60	0.73	0.75	0.38	0.47	0.81	0.75	0.84	0.83	0.85
Man	0.37	0.56	0.54	0.54	0.66	0.72	0.71	0.50	0.50	0.76	0.74	0.76	0.77	0.78
Monarch	0.31	0.60	0.55	0.53	0.69	0.81	0.83	0.47	0.80	0.86	0.88	0.90	0.89	0.90
Napoli	0.49	0.72	0.69	0.61	0.69	0.70	0.68	0.67	0.66	0.77	0.70	0.73	0.75	0.80
Peppers	0.36	0.54	0.52	0.54	0.65	0.77	0.77	0.46	0.36	0.82	0.82	0.83	0.84	0.85
Zelda	0.35	0.61	0.58	0.55	0.70	0.80	0.82	0.51	0.77	0.86	0.85	0.87	0.86	0.86

show the SSIM and PSNR values of the despeckled standard images using the proposed and the standard methods. The best value of the SSIM and PSNR are shown in bold and the second-best value of the SSIM and PSNR are shown in red color

The SAR-BM3D filter shows the best despeckling in the Barbara image (PSNR = 28.32 dB - the best value), Airplane image (PSNR = 28.10 dB - the best value), Hill image (PSNR = 28.30 dB - the best value), and House image (PSNR = 29.83 dB - the best value). Nevertheless, the proposed method in the Barbara image, Airplane image, and House image demonstrate second-best values. The proposed method of Choi et al. [1] shows the best despeckling in the Lena image (PSNR = 30.13 dB), Man image (PSNR = 28.55 dB), Monarch image (PSNR = 29.64 dB), and Zelda image (PSNR = 32.77 dB). However, SAR-BM3D in the Lena image shows slightly smaller values of PSNR than the method proposed by Choi et al. (PSNR = 29.91 dB - second-best value) and the proposed method in the Man image (PSNR = 28.00 dB), Monarch image (PSNR = 29.59 dB), and Zelda image (PSNR = 32.58 dB) show second-best values. The PSNR values of the proposed method exhibit the best performance of despeckling in the images (Boat = 28.24 dB; Cameraman = 28.43 dB; Fruits = 27.79 dB; Napoli = 26.83 dB and Peppers = 28.53 dB)

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 et al. provides the best edge preservation performance in Fruits = 0.78 and Hill = 0.73. SAR-BM3D provide the highest edge preservation performance, with Zelda = 0.87, Monarch = 0.90, House = 0.84, Hill = 0.73 Fruits = 0.78, Barbara = 0.84, and Airplane = 0.84. 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. The proposed method and SAR-BM3D exhibit the same edge preservation performance in Monarch = 0.90, Fruits = 0.78, and Airplane = 0.84. Table 4 and Table 5 confirm that the proposed method outcomes represent an excellent performance compared to the existing standard methods.

Table 6. The number of best, second best, and the sum of both.

Filters	Best	Second Best	Total
Proposed Method	14 (41%)	11 (34%)	25 (38%)
SARD-BM3D	11 (32%)	4 (12%)	15 (23%)
Choi at al	6 (17%)	12 (37%)	18 (27%)
SRAD	3 (8%)	4 (12%)	6 (9%)
SRAD-Guided	0 (0%)	1 (3%)	1 (1%)
Total	34	32	65

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 10 exhibits the comparison among the filtering result images of GF, Frost, Lee, bitonic, WLS, NLLR, ADMSS, SRAD, SRAD-Guided, SAR-BM3D filters, the proposed method of Choi et al., and our proposed method, respectively.

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.

5. 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 (Figure 11, Figure 12, and Figure 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. Equivalent number of looks (ENL) results for SAR image 1.

	Noisy	NLM	Guided	Frost	Lee	Bitonic	WLS	NLLR	ADMSS	SRAD	SRAD-Guided	SAR-BM3D	Choi at al	Proposed
ROI 1	14.3256	29.53	16.2	48.8	62	99.3	207.6	21.2	201.6	146.91	174.02	186.54	205.89	370.79
ROI 2	16.6041	28.66	13.1	39.4	51	80.6	180.4	20.56	124.8	117.17	141.3	129.35	160.67	208.54

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.

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. ENL and STD results for SAR image 2.

	Noisy		Bilateral		Fast Bilateral		GF		WLS		DPAD		SRAD		SAR-BM3D		Proposed Method
	ENL	STD	ENL	STD	ENL	STD	ENL	STD	ENL	STD	ENL	STD	ENL	STD	ENL	STD	ENL	STD
ROI 1	7.85	12.75	48.28	5. 07	81.860	3.827	78.75	3.80	137.8	2.901	9.36	11.54	9.783	11.27	26.6	7.119	88.624	3.799
ROI 2	39.5	19.62	333.7	6.73	617.36	4.957	201.6	8.66	2045	2.675	165.2	9.586	179.6	9.171	597	5.056	1107.5	3.658

). 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. The parameters of different filters used in this comparison.

Methods	Parameters
Guide	nhoodSize = 8; smoothValue = 0.01 × diff(getrangefromclass(A))2;
SAR-BM3D	Number of looks = 1
Bilateral	Windows size=3, spatial parameter = 2, Intensity parameter = 1.11.
Fast Bilateral	spatial parameter= 3, Intensity parameter=100.
WLS	Lambda = 0.5
DPAD	Noise Estimation Method = 5, The statistics for noise estimation are estimated on a 5 x 5 square window, Simplified SRAD = ’aja’

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.

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. PSNR, SNR, SSIM, and MAE results for SAR image 3 (The best value is shown in bold and the second-best value is shown in red color).

Filters	Noise Variance	PSNR	SNR	SSIM	MAE	Noise Variance	PSNR	SNR	SSIM	MAE
Proposed Method	0.04	30.5096	17.8982	0.7288	0.0206	0.06	30.2008	17.5895	0.7329	0.0211
SRAD		30.4319	17.8905	0.7117	0.0208		29.9429	17.3315	0.7768	0.0221
DPAD		31.0851	18.4737	0.8074	0.0196		29.9584	17.3470	0.7779	0.0222
SARBM3D		30.1945	17.5832	0.7234	0.0216		29.8910	17.2796	0.7202	0.0224
WLS		25.7167	13.1054	0.6390	0.0306		25.9700	13.3586	0.6480	0.0297
Guided		28.3137	15.702	0.6879	0.0255		28.0553	15.4440	0.6842	0.0261
Bilateral		28.1968	15.5854	0.6923	0.0243		28.1085	15.4972	0.6886	0.0246
Fast Bilateral		27.4941	14.8827	0.6603	0.0264		27.4814	14.8700	0.6633	0.0264
Proposed Method	0.08	29.7943	17.1829	0.7353	0.0216	0.1	29.3930	16.7816	0.7325	0.0222
SRAD		29.1088	16.4974	0.7530	0.0241		28.4999	15.8885	0.7309	0.0257
DPAD		29.2707	16.6594	0.7560	0.0238		28.6795	16.0682	0.7347	0.0253
SARBM3D		29.5661	16.9547	0.7187	0.0232		29.2430	16.6316	0.7168	0.0241
WLS		26.1780	13.5666	0.6565	0.0291		26.3455	13.7341	0.6621	0.0286
Guided		27.7338	15.1224	0.6769	0.0269		26.7039	14.0926	0.6646	0.0311
Bilateral		28.0322	15.4208	0.6861	0.0249		27.9592	15.3478	0.6822	0.0252
Fast Bilateral		27.4509	14.8395	0.6658	0.0263		27.4259	14.8145	0.6665	0.0264

). 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.

6. Computational Complexity

The time consumption of the proposed and the standard methods for 17 images are shown in

Table 11. Computational complexity results (in seconds) of the despeckling methods for each standard image (512 × 512 and 256 × 256). (the second-best value is shown in red color.).

Images	NLM	Guided	Frost	Lee	Bitonic	WLS	NLLR	ADMSS	SRAD	SARD-Guided	SAR-BM3D	Choi at al	Proposed
Airplane	0.48	0.16	1.86	6.41	0.09	3.51	1052.12	196.87	5.51	5.92	61.50	5.70	2.31
Baboon	0.48	0.11	2.00	7.29	0.10	0.48	1030.23	173.14	2.45	2.61	59.84	2.76	2.24
Barbara	0.50	0.12	2.05	7.28	0.08	1.00	1003.88	162.76	3.44	3.74	59.36	3.74	2.31
Boat	0.48	0.11	2.01	7.28	0.09	0.98	1007.25	174.22	5.06	5.48	61.07	5.36	2.32
Camera-man	0.12	0.08	0.52	1.88	0.03	0.46	211.28	21.64	1.55	1.21	14.45	1.91	0.40
Fruits	0.48	0.11	2.03	7.31	0.09	0.97	1012.13	181.41	7.40	7.85	62.17	7.84	2.31
Hill	0.48	0.11	1.98	7.25	0.09	0.99	1061.75	162.39	4.98	5.62	61.38	5.28	2.19
House	0.12	0.09	0.53	1.92	0.03	0.49	231.46	28.01	1.54	1.05	14.34	1.83	0.42
Lena	0.48	0.16	1.86	6.47	0.10	1.00	1081.19	170.44	7.53	8.03	60.16	7.71	2.25
Man	0.48	0.11	1.99	7.32	0.09	1.09	1057.03	165.61	5.23	5.70	60.15	5.40	2.24
Monarch	0.73	0.13	2.85	9.77	0.12	1.51	1661.38	277.26	8.48	5.96	87.94	8.93	3.24
Napoli	0.50	0.12	1.90	6.64	0.08	1.07	1060.22	168.11	4.02	4.10	59.55	4.31	2.28
Peppers	0.12	0.09	0.50	1.71	0.03	0.50	218.14	26.96	1.04	1.16	14.49	1.32	0.40
Zelda	0.48	0.12	1.88	6.88	0.09	0.99	1001.87	164.50	7.10	7.45	59.57	7.32	2.35
Avg.	0.42	0.12	1.71	6.10	0.08	1.07	906.42	148.09	4.67	4.71	52.57	5.06	1.92

,

Table 12. The runtime of all the filters in the proposed method. (the second-best value is shown in red color.).

Images	EAWF	EGF(First Time)	EGF(Second Time)	WLS	Total
Airplane	0.0295	0.1024	0.0866	2.0926	2.31
Baboon	0.0534	0.2491	0.0798	1.8591	2.24
Barbara	0.0314	0.1072	0.0969	2.0737	2.31
Boat	0.0299	0.0998	0.0913	2.0994	2.32
Camera-man	0.0172	0.1070	0.0169	0.2597	0.40
Fruits	0.0396	0.2182	0.0790	1.9733	2.31
Hill	0.0436	0.2432	0.0913	1.8118	2.19
House	0.0063	0.0237	0.0219	0.3681	0.42
Lena	0.0375	0.2024	0.0811	1.9295	2.25
Man	0.0401	0.2136	0.0779	1.9077	2.24
Monarch	0.0426	0.2385	0.1060	2.8538	3.24
Napoli	0.0300	0.1678	0.0740	2.0083	2.28
Peppers	0.0059	0.0241	0.0219	0.3505	0.40
Zelda	0.0398	0.2167	0.0813	2.0123	2.35
Avg.	0.0319	0.1581	0.0718	1.6857	1.92

,

Table 13. Computational complexity results of the despeckling methods for the real SAR images 1 (512 × 512).

	NLM	Guided	Frost	Lee	Bitonic	WLS	NLLR	ADMSS	SRAD	SRAD-Guided	SAR-BM3D	Choi at al	Proposed
SAR image 1	20.47	0.19	1.73	6.23	0.12	0.71	1071.8	191.19	7.09	7.48	62.95	7.45	2.76

,

Table 14. Computational complexity results of the despeckling methods for the real SAR image 2 (1323 × 803).

	Bilateral	Fast Bilateral	GF	WLS	DPAD	SRAD	SAR-BM3D	Fang at al	Proposed
SAR image 2	25.18409	1.173549	0.465048	8.785592	34.505417	34.095685	1051.7271	198.9801	11.207373

,

Table 15. Computational complexity results of all the filters in the proposed method for the real SAR image 1 (512 × 512);.

	EAWF	EGF (First Time)	EEGF (Second Time)	WLS	Total
SAR image 1	0.0341666	0.10135565	0.09835454	2.52735569	2.76123248

,

Table 16. Computational complexity results of all the filters in the proposed method for the real SAR image 2 (1323 × 803).

	EAWF	EGF (First time)	EEGF (Secondd titime)	WLS	Total
SAR image 2	0.092552	0.682677	0.933745	9.498399	11.207373

,

Table 17. Computational complexity results of the despeckling methods for the real SAR images 3 (600 × 418).

Filters	Noise Variance	Run Time	Noise Variance	Run Time
Proposed Method	0.04	3.51532	0.06	2.87514
SRAD		8.55225		8.67667
DPAD		9.39500		8.93444
SARBM3D		286.548		283.948
WLS		1.95118		1.69643
Guided		0.12702		0.14519
Bilateral		7.22676		6.94197
Fast Bilateral		0.42709		0.39429
Proposed Method	0.08	2.86262	0.1	3.98923
SRAD		9.02507		8.67005
DPAD		8.75984		8.21100
SARBM3D		284.064		285.219
WLS		1.71835		1.66355
Guided		0.13848		0.15345
Bilateral		7.38375		8.77612
Fast Bilateral		0.44584		0.79916

and

Table 18. Computational complexity results of all the filters in the proposed method for the real SAR image 3 (600 × 418).

Noise Variance	EAWF	EGF (First Time)	EGF (Second Time)	WLS	Total
0.04	0.03511	0.710129	1.078701	1.691	3.515
0.06	0.03385	0.443889	0.565306	1.832	2.875
0.08	0.03495	0.441253	0.604423	1.782	2.863
0.1	0.03799	1.500044	0.571564	1.871	3.981
	0.03548	0.773828	0.704998	1.794	3.31

. According to Table 11, Table 12, and Table 13, the proposed method is faster than Lee, NLLR, ADMSS, SRAD, SRAD-guided, SAR-BM3D, and Choi et al. In addition, according to Table 14 and Table 16, the proposed method is faster than the bilateral filter, DPDA, SRAD, SRAD-guided, SAR-BM3D, and Fang et al. The average time cost of the proposed method with fourteen images and three SAR images is about 1.92 s, 2.76 s, 11.20 s, and 3.31 s, respectively. In addition, for precise examination, the runtimes of all sub-filters of the proposed method are studied (Table 12, Table 15, Table 16 and Table 18)

7. 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 Table 4, Table 5, and Table 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 Table 11, Table 12, Table 13, Table 14, Table 15 and Table 16, the proposed method is faster than Lee, NLLR, ADMSS, SRAD, SRAD-guided, SAR-BM3D, Bilateral filter, DPAD, the proposed method of Fang et al., and the proposed method of Choi et al. The average time cost of the proposed method for fourteen images and three SAR images is about 1.92 s (image size: 512 × 512 and 256 × 256), 2.76 s (image size: 512 × 512), 11. 20 s (image size: 1323 × 803) and 3.31 s (image size: 600 × 418) respectively. The experimental outcome shows that the proposed method exhibits outstanding despeckling and low time complexity while preserving edge information.

8. 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.