# An Advanced SAR Image Despeckling Method by Bernoulli-Sampling-Based Self-Supervised Deep Learning
## 1 Introduction
Hence, it is not ideal to obtain despeckled SAR images by training the network on synthetic speckled data in practical situations. A domain gap problem has been exposed: the despeckling networks perform well on the data, which are from a domain similar to the training data (i.e., synthetic speckled images), but perform poorly on the testing data (i.e., real SAR images). To address the problem that supervised learning-based CNN methods need to require \"Noisy2 Clean\" image pairs to train denoising networks, [PERSON] et al. [37] proposed a novel training strategy (named Noise2 Noise). It demonstrated that denoised images could be generated with the networks trained on \"Noisy2 Noisy\" image pairs, consisting of noisy inputs and noisy targets. They both contain the same underlying clean ground truth and are corrupted by the independent and identical noise. Its basic idea is that the mean squared error (MSE) loss function is minimized by the expected value of the targets. Hence, the Noise2 Noise strategy is suitable for the noisy images whose expected value is equal to that of the underlying clean ground truth, for example the noisy images corrupted by additive white Gaussian noise (AWGN). Inspired by this, [PERSON] et al. [38] proposed a noisy  
Figure 1: Illustration of the differences between optical and SAR images. (**a**,**b**) are the original optical image acquired by _Sentinel-2_ and the corresponding single-channel grey image. (**c**) is the SAR image acquired by _Sentinel-1_. Though these images were acquired from the same scene, they are different in their image characteristics, e.g., the grey-level distribution and the scattering phenomena. reference-based SAR deep learning (NR-SAR-DL) filter, which used multitemporal SAR images to train the despeckling network. These images (called Speckled2 Speckled image pairs) were acquired from the same scene by the same sensor. NR-SAR-DL has outstanding despeckling performance on real multitemporal SAR data, especially in preserving point targets and the radiometrics. However, though NR-SAR-DL integrates temporal stationarity information into the loss function, its effectiveness is still affected by the training errors caused by temporal variations. When neither \"Speckled2 Clean\" nor \"Speckled2 Speckled\" image pairs are available, training the CNN-based despeckling network becomes challenging. Recently, [PERSON] et al. [39] proposed a dropout-based scheme (named Self2 Self) for image denoising with only single noisy images. In the Self2 Self strategy, a denoising CNN with dropout was trained on the Bernoulli-sampled instances of noisy images. For the noisy images corrupted by the AWGN, the denoising performance of Self2 Self is comparable to that of \"Noisy2 Clean\", which provides the possibility for just using real speckled SAR images to train a deep despeckling network. In this paper, we aim to solve such a problem: training a deep despeckling network requires clean SAR ground truth images that are difficult to obtain in real-world conditions. By solving this problem, the deep despeckling network can be trained on real SAR images instead of synthetic speckled images. To this end, inspired by Self2 Self, we propose an advanced SAR image despeckling method by virtue of Bernoulli-sampling-based self-supervised deep learning, namely SSD-SAR-BS. Our main contributions are summarized as follows:  
* To address the problem that no clean SAR images can be employed as targets to train the deep despeckling network, we propose a Bernoulli-sampling-based self-supervised despeckling training strategy, utilizing the known speckle noise model and real speckled SAR images. The feasibility is proven with mathematical justification, combining the characteristic of speckle noise in SAR images and the mean squared error loss function;
* A multiscale despeckling network (MSDNet) was designed based on the traditional UNet, where shallow and deep features are fused to recover despeckled SAR images. Dense residual blocks are introduced to enhance the feature extracting ability.