Multiply Complementary Priors for Image Compressive Sensing Reconstruction in Impulsive Noise

Abstract

Impulsive noise is always present in real-world image Compressive Sensing (CS) acquisition systems, where existing CS reconstruction performance may seriously deteriorate. In this paper, we propose a robust CS formulation for image reconstruction to suppress outliers in the presence of impulsive noise. To address this issue, we consider a novel truncated-Cauchy loss function as the metric of residual error to elevate the reconstruction robustness. Specifically, we design a complementary priors model to incorporate nonconvex nonlocal low-rank prior and deep denoiser prior for high-accuracy image reconstruction. By means of the half-quadratic (HQ) optimization theory and generalized soft-thresholding (GST) technique, we also develop an alternative optimization algorithm for solving the induced nonconvex optimization problem. Numerical simulations demonstrate the robustness and accuracy of the proposed robust CS method compared to some recent CS methods for image reconstruction in impulsive noise.