Image compressed sensing based on nonlocal similarity and alternating iterative optimization algorithm

Compressed Sensing is a new technique for simultaneous data sampling and compression. It breaks through the limits to Nyquist sampling theorem which needs very wide signal bandwidth when sampling. Currently, compressed sensing system used the prior that the image has sparsity in some transform domain to reconstruct the original image from fewer measurements. In this paper, the nonlocal similarity was used in image compressed sensing and combined with the sparsity as prior. Hence, the neighborhood structure information of the image pixels and the similarity of images are fully used. On the basis of the nonlocal similarity prior and the image has sparsity in some transform domain, a new image compressed sensing algorithm based on nonlocal similarity and alternating iterative optimization algorithm is proposed. The proposed algorithm solved the image compressed sensing problem by dealing with the following two optimization problems alternatively: sparsity optimization problem and the nonlocal similarity optimization problem. And the two optimization problems are solved respectively by the iterative thresholding algorithm and nonlocal total variation. Simulation results show that the performance of the proposed algorithm has significant performance improvement in visual quality of the reconstructed image and peak signal-to-noise ratio.