A Douglas–Rachford Splitting Approach to Compressed Sensing Image Recovery Using Low-Rank Regularization

Abstract

In this paper, we study the compressed sensing (CS) image recovery problem. The traditional method divides the image into blocks and treats each block as an independent sub-CS recovery task. This often results in losing global structure of an image. In order to improve the CS recovery result, we propose a nonlocal (NL) estimation step after the initial CS recovery for denoising purpose. The NL estimation is based on the well-known NL means filtering that takes an advantage of self-similarity in images. We formulate the NL estimation as the low-rank matrix approximation problem, where the low-rank matrix is formed by the NL similarity patches. An efficient algorithm, nonlocal Douglas-Rachford (NLDR), based on Douglas-Rachford splitting is developed to solve this low-rank optimization problem constrained by the CS measurements. Experimental results demonstrate that the proposed NLDR algorithm achieves significant performance improvements over the state-of-the-art in CS image recovery.