# An Advanced SAR Image Despeckling Method by Bernoulli-Sampling-Based Self-Supervised Deep Learning
## 3 Experimental Results and Analysis
### Despeckling Experiments on Real-World SAR Data
Cx can estimate the texture preservation performance and can be given as:  
\[\text{Cx}=\frac{\sigma_{\mathbf{x}^{\text{HR}}}}{\mu_{\mathbf{x}^{\text{HR}}}}, \tag{22}\]  
where the lower Cx value represents better texture preservation. The MoR can measure how well the radiometric preservation is in the despeckled results, which is defined as:  
\[\text{MoR}=\frac{1}{WH}\sum_{w=1}^{W}\sum_{h=1}^{H}\frac{\mathbf{Y}_{w,h}^{ \text{HR}}}{\mathbf{x}_{w,h}^{\text{HR}}}. \tag{23}\]  
For the ideal radiometric preservation, the MoR value should be 1. Table 3 provides the quantitative comparison. Figures 11-14 present the corresponding magnified despeckling results. From Table 3, we can see that the PPB had a strong speckle noise reduction ability in homogeneous regions. However, it lost the most detailed features of the heterogeneous regions presented in Figures 11-14b. The speckle noise removal ability of SAR-BM3D was not as strong as that for the PPB, but it surpassed the PPB by a large margin in terms of detailed feature preservation. Similar to the synthetic speckled dataset experiment, a critical problem of SAR-BM3D is that its results presented the blocking phenomenon. This phenomenon can be observed in Figures 11-13c. The mottled blocking artefacts should not appear in the ideal despeckled results. The performance of ID-CNN, SAR-DRN, and SAR-RDCP on real SAR images was not as good as on synthetic speckled images. This can be confirmed in terms of speckle noise reduction in the homogeneous regions (seen in Table 3). Furthermore, from Figures 11-14d-f, we can see that there were some chaotic line-like artefacts in their despeckled results. These phenomena are called the domain gap problem. These methods adopted supervised learning, so their despeckling networks can only be trained using synthetic speckled data from optical images. However, due to the differences in the imaging mechanisms, SAR images have many characteristics that are not present in optical images, including scattering characteristics. When employing the feature extraction capability learned from synthetic speckled images on a different data domain (i.e., real SAR images), they showed nonoptimal despeckling performance and generated some unnatural artefacts in their despeckled results. Figure 11: Magnified despeckling results for the _Sentinel-1_ #1 image. (**a**) Speckled. (**b**) PPB. (**c**) SAR-BM3D. (**d**) ID-CNN. (**e**) SAR-DRN. (**f**) SAR-RDCP. (**g**) Proposed SSD-SAR-BS. Figure 12: Magnified despeckling results for the _Sentinel-1_ #2 image. (**a**) Speckled. (**b**) PPB. (**c**) SAR-BM3D. (**d**) ID-CNN. (**e**) SAR-DRN. (**f**) SAR-RDCP. (**g**) Proposed SSD-SAR-BS. Figure 14: Magnified despeckling results for the _TernSAR-X_ #2 image. (**a**) Speckled. (**b**) PPB. (**c**) SAR-BM3D. (**d**) ID-CNN. (**e**) SAR-DRN. (**f**) SAR-RDCP. (**g**) Proposed SSD-SAR-BS. Figure 13: Magnified despeckling results for the _TernSAR-X_ #1 image. (**a**) Speckled. (**b**) PPB. (**c**) SAR-BM3D. (**d**) ID-CNN. (**e**) SAR-DRN. (**f**) SAR-RDCP. (**g**) Proposed SSD-SAR-BS. In contrast, our proposed SSD-SAR-BS learned the despeckling ability from real SAR images, thereby fundamentally avoiding the domain gap problem. Specifically, it showed good speckle noise suppression, texture preservation, and radiometric preservation of homogeneous regions, according to the larger ENL values, lower Cx values, and MoR values closer to one. This can also be verified in Figure 14g (the regions marked by red circles). Besides, our proposed SSD-SAR-BS also avoided generating artefacts while preserved the original features. Specifically, from Figures 12d-g, we can observe that our proposed SSD-SAR-BS provided smooth homogeneous regions; in contrast, chaotic line-like artefacts can be significantly found in the results of ID-CNN, SAR-DRN, and SAR-RDCP. Meanwhile, the dense small points in red circles can also be clearly found in the result of our proposed SSD-SAR-BS.