Nonlocal low-rank plus deep denoising prior for robust image compressed sensing reconstruction

It is challenging for current compressive sensing (CS) approaches to reconstruct image from compressed observations with impulsive noise and outliers, termed robust image CS problem. In this paper, we propose a novel reconstruction model for the robust image CS reconstruction problem in the presence of impulsive noise. To ensure high-quality image reconstruction, we develop a nonlocal low-rank plus deep denoising prior model to simultaneously capture the nonlocal self-similarity (NSS) and deep prior, leading to a complementary reconstruction effect. Moreover, the robust M-estimator is utilized to suppress the outliers, which can strongly improve the robustness to impulsive noise. Considering the nonconvexity and complexity, both the half-quadratic (HQ) strategy and the alternating minimization method are employed to minimize the resulting large-scale optimization problem. Extensive experiments have demonstrated the effectiveness and superiority of our method significantly than the existing state-of-the art CS methods in terms of both visual quality and quantitative indexes under impulsive noise. •A robust image CS reconstruction approach with nonlocal low-rank plus deep denoising prior is proposed.•An efficient optimization framework based on half-quadratic (HQ) theory and the alternative minimizing scheme is developed.•The superior reconstruction performance is confirmed over various advanced CS algorithms.