Image compressive sensing via Truncated Schatten-p Norm regularization

Abstract

Low-rank property as a useful image prior has attracted much attention in image processing communities. Recently, a nonlocal low-rank regularization (NLR) approach toward exploiting low-rank property has shown the state-of-the-art performance in Compressive Sensing (CS) image recovery. How to solve the resulting rank regularization problem which is known as an NP-hard problem is critical to the recovery results. NLR takes use of logdet as a smooth nonconvex surrogate function for the rank instead of the convex nuclear norm. However, logdet function cannot well approximate the rank because there exists an irreparable gap between the fixed logdet function and the real rank. In this paper, Truncated Schatten-p Norm regularization, which is used as a surrogate function for the rank to exploit the benefits of both schatten-p norm and truncated nuclear norm, has been proposed toward better exploiting low-rank property in CS image recovery. In addition, we have developed an efficient iterative scheme to solve the resulting nonconvex optimization problem. Experimental results have demonstrated that the proposed algorithm can significantly outperform the existing state-of-the-art image CS methods.