# An Advanced SAR Image Despeckling Method by Bernoulli-Sampling-Based Self-Supervised Deep Learning
## 1 Introduction
However, due to the changes in different time sequences and the scene registration, it was not entirely reliable to treat the multilook images as the clean targets, leading to a suboptimal rejection of speckle noise;  
(2) Synthetic speckled data: A more common strategy of deep-learning-based SAR image despeckling methods is to construct synthetic speckled data for training. These methods all adopt supervised learning by using \"Speckled2 Clean\" image pairs. In other words, speckle-free single-channel grey optical images (e.g., UC Merced land-use dataset [35]) are employed as clean targets, and speckled inputs are generated by adding speckle noise to the corresponding single-channel grey optical images. Specifically, image despeckling CNN (ID-CNN) [28] employs eight convolutional layers along with the rectified linear unit (ReLU) activation function and the batch normalization layers. In addition, a division residual layer with the skip connection is used to output despeckled images, where the speckled inputs are divided by the estimated speckle noise. The SAR dilated residual network (SAR-DRN) [29] implements a seven-layer lightweight network with dilated convolutions, enlarging the receptive field while keeping the filter size. Unlike ID-CNN, SAR-DRN employs residual learning. In other words, the network outputs are the estimated speckle noise of speckled inputs rather than despeckled images. Then, the loss function is calculated between the estimated and the residual speckle noise. The residual speckle noise is obtained by subtracting the clean targets from the corresponding speckled inputs. The multiscale recurrent network (MSR-Net) [30] was presented with multiscale cascaded subnetworks. Each subnetwork consists of an encoder, a decoder, and a convolutional long short-term memory unit. In addition, the multiscale recurrent and weight sharing strategies were adopted to increase network capacity. The hybrid dilated residual attention network (HDRANet) [31] and SAR-DRN both utilize dilated convolutions to enlarge the receptive field. Different from SAR-DRN, HDRANet proposes hybrid dilated convolution, which can avoid causing gridding artefacts. The attention module via a residual architecture was also introduced to improve network performance. In particular, the spatial and transform domain CNN (STD-CNN) [32] fuses spatial and wavelet-based transform domain features for SAR image despeckling with rich details and a global topology structure. A multiconnection network incorporating wavelet features (MCN-WF) [33] also references the wavelet transform. By using wavelet features, the loss function was redesigned to train a multiconnection network based on dense connections. Considering the distribution characteristics of SAR speckle noise, the SAR recursive deep CNN prior (SAR-RDCP) [34] combines the strong mathematical basis of traditional variational models and the nonlinear end-to-end mapping ability of deep CNN models. The whole SAR-RDCP model consists of two subblocks: a data-fitting block and a predenoising residual channel attention block. By introducing a novel despeckling gain loss, two subblocks are jointly optimized to achieve the overall network training. The advantage of using synthetic speckled data is that they can contain a large number of \"Speckled2 Clean\" image pairs. This advantage allows deep CNN models to be trained stably without overfitting and to learn the complex nonlinear mapping relationships between speckled inputs and clean targets. However, due to the difference in the imaging mechanism, optical images have shown many differences from SAR images in terms of grey-level distribution, spatial correlation, dynamics, power spectral density, etc. [18]. Many unique characteristics (e.g., scattering phenomena) of SAR images are neglected in the training process. An illustration of the differences between optical and SAR images is presented in Figure 1, provided by the Sen1-2 dataset [36].