A fine-grain nonlocal weighted average method for image CS reconstruction

Compressive sensing can acquire a signal at a sampling rate far below the Nyquist sampling rate if signal is sparse in some domain. However, signal reconstruction from its observations is challenging because it is an implicit ill-pose problem in practice. As classical CS reconstruction methods, total variation (TV) and iteratively reweighted TV (ReTV) methods only exploit local image information, which results in some loss of image structures and causes blocking effect. In this paper, we observe there are abundant nonlocal repetitive structures in nature image, so we propose a novel fine-grain nonlocal weighted average method for nature image CS reconstruction, and we take full use of the nonlocal repetitive structures to recover image from the observations. Besides, an efficient iterative bound optimization algorithm which is stably convergent in our experiments is applied to the above CS reconstruction. The experimental results of different nature images demonstrate that our proposed algorithm can outperform the existing classical nature image CS reconstruction algorithms in Peak-Signal-Noise-Ratio (PSNR) and subjective evaluation.