Robust image compressive sensing based on m-estimator and nonlocal low-rank regularization

The current compressive sensing (CS) methods based on nonlocal low-rank regularization have shown the state-of-art recovery performance. However, these methods exploiting l2-norm as the cost function depends heavily on the Gaussianity assumption of noise. The recovery performance will degrade when impulsive noise occurs in acquisition process. In this paper, we propose a robust image CS recovery framework combining m-estimator with nonlocal low-rank regularization, to investigate the situation where measurements are corrupted by impulsive noise. Since l2-norm is mainly responsible for the performance degradation under impulsive noise, we substitute it with the robust Welsch m-estimator which has shown great ability of managing impulsive noise in a wide range of applications. As for low-rank regularization, we utilize the truncated schatten-p norm which has been verified to be the best surrogate function in the open literature. Furthermore, we have developed a framework based on alternating direction multiplier method (ADMM) and half-quadratic (HQ) theory to solve the resulting nonconvex problem. Extensive experiments have demonstrated that the proposed method significantly outperforms the existing state-of-art methods in terms of both PSNR index and visual quality under impulsive noise.