# 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  
In this section, the despeckling performance of our proposed SSD-SAR-BS is verified using real SAR images. They are:  
(1) _Sentinel-1_[50]: This is a low-resolution (about 10 m) SAR system with the C-band, provided by the _Copernicus data hub_ of the European Space Agency (ESA), whose data can be downloaded from [[https://scihub.copernicus.eu/](https://scihub.copernicus.eu/)]([https://scihub.copernicus.eu/](https://scihub.copernicus.eu/)) (accessed on 23 October 2020). The download data used were single-look complex with interferometric wide swath (IWS) mode. In the _Sentinel-1_ despeckling experiment, Table 14 gives the downloaded file name list of the _Sentinel-1_ data used. Then, a total of 221,A36 one-look (i.e., \(L=1\)) image patches with a size of 64 \(\times\) 64 pixels were used to train our proposed SSD-SAR-BS. In addition, we selected two one-look images (denoted as _Sentinel-1 #1_ and _Sentinel-1 #2_) with a size of 1024 \(\times\) 1024 pixels. They were not included in the training data for the independent test. There were many representative SAR features in the test images, such as homogeneous region, detailed texture, point target, and strong edge;  
(2) _TerraSAR-X_[51]. This is a high-resolution (about three meters) SAR system with the X-band, provided by the TerraSAR-X ESA archive collection, whose data can be downloaded from [[https://tpm-ds.e.esa.int/oads/access/collection/TerraSAR-X](https://tpm-ds.e.esa.int/oads/access/collection/TerraSAR-X)]([https://tpm-ds.e.esa.int/oads/access/collection/TerraSAR-X](https://tpm-ds.e.esa.int/oads/access/collection/TerraSAR-X)) (accessed on 22 August 2020). The imaging mode of the download data used is StripMap (SM). In the _TerraSAR-X_ despeckling experiment, Table 15 gives the downloaded file name list of the _TerraSAR-X_ data used. Then, a total of 222,753 one-look (i.e., \(L=1\)) image patches with a size of 64 \(\times\) 64 pixels were used to train our proposed SSD-SAR-BS. In addition, we selected two one-look images (denoted as _TerraSAR-X #1_ and _TerraSAR-X #2_) with a size of 1024 \(\times\) 1024 pixels. Similarly, they were not included in the training data. Further  
Figure 10: Magnified results for synthetic speckled images. In the subgraph number, (**1**) denotes _Airport_, (**2**) denotes _Beach_, (**3**) denotes _Parking_, and (**4**) denotes _School_. (**a**) Speckled. (**b**) PPB. (**c**) SAR-BM3D. (**d**) ID-CNN. (**e**) SAR-DRN. (**f**) SAR-RDCP. (**g**) Proposed SSD-SAR-BS. (**h**) Speckle-free reference. more, there were many complicated features in the test images to examine the despeckling performance, such as homogeneous regions, dense lines, and strong edges. To make the despeckled results smoother, we added total variation (TV) regularization \(\mathcal{L}_{\text{TV}}\) to the loss function, which is described as:  
\[\mathcal{L}=\mathcal{L}_{\text{MSE}}+\lambda_{\text{TV}}\mathcal{L}_{\text{TV }}, \tag{20}\]  
\[\mathcal{L}_{\text{TV}}=\frac{1}{M}\sum_{m=1}^{M}\sum_{w=1}^{W-1}\sum_{h=1}^{ H-1}(|f_{\theta}(\hat{\mathbf{Y}}^{(m)})_{w+1,h}-f_{\theta}(\hat{\mathbf{Y}}^{(m )})_{w,h}| \tag{21}\]  
where \(\lambda_{\text{TV}}\) is the tradeoff weight for the TV regularization. \(\mathcal{L}_{\text{TV}}\) minimizes the absolute differences between neighbouring pixel values. To avoid detail loss, \(\lambda_{\text{TV}}\) was set to be far less than 1, specifically, \(\lambda_{\text{TV}}=0.0001\). Due to speckle-free (clean) SAR images not being able to be used as the reference, the PSNR and SSIM were no longer applicable for the real SAR despeckling quantitative evaluation. Except for the above ENL index, we employed another two nonreference indexes. They are the coefficient of variation (Cx) [52] and the mean of ratio (MoR) [17], calculated using the homogeneous region patch of despeckled results.