Co-Robust-ADMM-Net: Joint ADMM Framework and DNN for Robust Sparse Composite Regularization

Symmetric α-stable (SαS) noise is a typical form of impulsive noise often generated in signal measurement and transmission systems. The problem of reconstructing an image from a small number of under-sampled data corrupted by impulsive noise is called robust compressive sensing (CS). In this paper, to effectively suppress the outliers and accurately reconstruct the image from compressive measured data in the presence of SαS noise, a novel composite robust alternating direction method of multiplier network-based CS algorithm is proposed. Specifically, we first employ the L
₁
-norm as the estimator to depress the influence of SαS noise, and then the ADMM framework is employed to address the resulting optimization problem. Moreover, a smoothing strategy is adopted to address the L
₁
-norm based non-smooth optimization problem. To exploit more prior knowledge and image features, a robust composite regularization model is proposed for training by the deep neural network (DNN). In the training phase, the DNN can be utilized to train the samples for the optimal parameters, the optimal shrinkage function and the optimal transform domain, which can be reserved as the network. In the reconstruction process, the obtained network can be employed for improving the reconstruction performance. Experiments show that our proposed algorithm can obtain higher reconstruction Peak signal-to-noise ratio than the existing state-of-the-art robust CS methods.