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 estimation step after the initial CS recovery for de-noising purpose. The nonlocal estimation is based on the well-known nonlocal means (NL) filtering that takes advantage of self-similarity in images. We formulate the nonlocal estimation as the low-rank matrix approximation problem where the low-rank matrix is formed by the nonlocal similarity patches. An efficient algorithm, Extended NonLocal Douglas-Rachford (E-NDLR), 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 E-NDLR algorithm achieves significant performance improvements over the state-of-the-art in CS image recovery.
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