Nonlocal Low-Rank Residual Modeling for Image Compressive Sensing Reconstruction

The nonlocal low-rank (LR) modeling has proven to be an effective approach in image compressive sensing (CS) reconstruction, which starts by clustering similar patches using the nonlocal self-similarity (NSS) prior into nonlocal image groups and then imposes an L-R penalty on each nonlocal image group. However, most existing methods only approximate the LR matrix directly from the degraded nonlocal image group, which may lead to suboptimal LR matrix approximation and thus obtain unsatisfactory reconstruction results. This paper proposes a novel nonlocal low-rank residual (NLRR) approach for image CS reconstruction, which progressively approximates the underlying LR matrix by minimizing the LR residual. To do this, we first use the NSS prior to obtain a good estimate of the original nonlocal image group, and then the LR residual between the degraded nonlocal image group and the estimated nonlocal image group is minimized to derive a more accurate LR matrix. To ensure the optimization is both feasible and reliable, we employ an alternative direction multiplier method (ADMM) to solve the NLRR-based image CS reconstruction problem. Our experimental results show that the proposed NLRR algorithm achieves superior performance against many popular or state-of-the-art image CS reconstruction methods, both in objective metrics and subjective perceptual quality.