# An Advanced SAR Image Despeckling Method by Bernoulli-Sampling-Based Self-Supervised Deep Learning
## 3 Experimental Results and Analysis
### Despeckling Experiments on Synthetic Speckled Data  
For a fair comparison, in the synthetic speckled data despeckling experiments, all deep-learning-based despeckling methods shared the same training dataset, which was built using optical remote sensing images from the UC Merced land-use dataset [35]. From this dataset, a total of 209,990 image patches with a size of \(64\times 64\) were extracted as the speckle-free target images. The corresponding speckled input images were generated according to (1) and (2), where the number of looks was randomly selected from \(\{1,2,4,8\}\). It is worth mentioning that our proposed SSD-SAR-BS did not see the speckle-free target images, and only speckled input images were needed for training. In contrast, other deep-learning-based methods (i.e., ID-CNN, SAR-DRN, and SAR-RDCP) all see the speckle-free target images in the training process. Furthermore, for testing, four optical remote sensing images from another dataset (i.e., the aerial image dataset (AID) [48]) were selected. They were _Airport_, _Beach_, _Parking_, and _School_, respectively. The corresponding single-look speckled input images were also generated according to (1) and (2). With the speckle-free target images, two classic fully referenced metrics (i.e., the peak signal-to-noise ratio (PSNR) and the structural similarity index (SSIM) [49]) were employed for the evaluation. The PSNR is defined as:  
\[\text{PSNR}=10\text{log}_{10}\frac{255^{2}}{\frac{1}{\text{W}\text{H}}\sum \limits_{w=1}^{W}\sum\limits_{h=1}^{H}(\mathbf{X}_{w,h}-\mathbf{X}^{\prime}_{ w,h})^{2}} \tag{17}\]  
where \(\mathbf{X}^{\prime}\) and \(\mathbf{X}\) denote the despeckled image and the corresponding speckle-free image with a size of \(W\times H\), respectively. \(\mathbf{X}^{\prime}_{w,h}\) and \(\mathbf{X}_{w,h}\) are the pixel value in \(\mathbf{X}^{\prime}\) and \(\mathbf{X}\), respectively. The larger PSNR value indicates the lower distortion of the despeckled images. The SSIM is calculated as:  
\[\text{SSIM}=\frac{(2\mu_{\mathbf{X}}\mu_{\mathbf{X}^{\prime}}+C_{1})(2\sigma_ {\mathbf{X}\mathbf{X}^{\prime}}+C_{2})}{(\mu\mathbf{x}^{2}+{\mu_{\mathbf{X}} }^{2}+C_{1})(\sigma\mathbf{x}^{2}+\sigma_{\mathbf{X}^{\prime}}^{2}+C_{2})} \tag{18}\]  
where \(\mu_{\mathbf{X}}\) and \(\mu_{\mathbf{X}^{\prime}}\) are the mean values of \(\mathbf{X}\) and \(\mathbf{X}^{\prime}\), respectively; \(\sigma_{\mathbf{X}}\) and \(\sigma_{\mathbf{X}^{\prime}}\) are the standard deviation values of \(\mathbf{X}\) and \(\mathbf{X}^{\prime}\), respectively; \(\sigma_{\mathbf{X}\mathbf{X}^{\prime}}\) represents the covariance value between \(\mathbf{X}\) and \(\mathbf{X}^{\prime}\); and \(C_{1}\) and \(C_{2}\) are added as two constants to avoid instability when \(\mu_{\mathbf{X}}{}^{2}+{\mu_{\mathbf{X}}}^{2}\) or \(\sigma_{\mathbf{X}}{}^{2}+{\sigma_{\mathbf{X}}}^{2}\) is close to zero. The larger SSIM value means better structural feature preservation. Except for the two fully referenced metrics (i.e., PSNR and SSIM), a nonreferenced metric (i.e., the equivalent number of looks (ENL) [17]) was employed to evaluate the speckle suppression performance, expressed as:  
\[\text{ENL}=\frac{(\mu_{\mathbf{X}^{\prime\text{HR}}})^{2}}{(\sigma_{\mathbf{X }^{\prime\text{HR}}})^{2}} \tag{19}\]  
where \(\mathbf{X}^{\prime\text{HR}}\) represents a homogeneous region patch of \(\mathbf{X}^{\prime}\). \(\mu_{\mathbf{X}^{\prime\text{HR}}}\) and \(\sigma_{\mathbf{X}^{\prime\text{HR}}}\) are the mean value and standard deviation value of \(\mathbf{X}^{\prime\text{HR}}\), respectively. The larger the ENL value, the better the speckle noise reduction is. Table 2 lists the quantitative evaluation results, with the best and second-best performance marked in bold and underlined. We can see that, among the traditional despeckling methods, SAR-BM3D was the one with better overall performance in the quantitative evaluation. Furthermore, deep-learning-based despeckling methods (especially SAR-DRN and SAR-RDCP) had a noticeable improvement compared to the traditional despeckling methods.