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To reconstruct natural images from compressed sensing (CS) measurements accurately and effectively, a CS image reconstruction algorithm based on hybrid-weighted total variation (HWTV) and nonlocal low-rank (NLR) is proposed. It considers the local smoothness and nonlocal self-similarity (NSS) in image, improves traditional hybrid total variation (TV) model, and constructs a new edge detection operator with mean curvature to adaptively select the TV. The HWTV combines the advantages of first-order TV and second-order TV to preserve the edges of the image and avoid the staircase effect in the smooth areas. And NLR can effectively reduce the redundant information and retain the structural information of the image. In addition, the proposed algorithm constructs prior regularization terms with improved HWTV model and NLR model, and utilizes soft threshold function and smooth but non-convex function to solve the TV and low-rank optimization problems, respectively. Finally, the alternative direction multiplier method (ADMM) iterative strategy is used to separate the target model into several sub-problems, and the most efficient methods are adopted to solve each sub-problem. Experimental results show that, compared with the state-of-the-art CS reconstruction algorithms, the proposed algorithm can achieve higher reconstruction quality, especially in the case of low sampling rates.

Hybrid-Weighted Total Variation and Nonlocal Low-Rank-Based Image Compressed Sensing Reconstruction