Accelerated Proximal Gradient Method for Image Compressed Sensing Recovery Using Nonlocal Sparsity

Compressed Sensing (CS) exploits sparsity of images to reconstruct them exactly from a small set of measurements. Recent studies have shown that nonlocal sparsity leads to superior results in CS recovery. In this paper, we first propose a new sparsity model, which is characterized as a function of the coefficients achieved by transforming the 3D array generated from a set of similar image patches. The function which we use is the nonconvex Garrote function. To efficiently solve the proposed corresponding optimization problem, we then employ an accelerated algorithm based on iterative proximal methods. Our reconstruction method exploits the benefits of both nonlocal sparsity and nonconvex optimization. Experimental results show effectiveness of the proposed method compared with the many existing algorithms in CS image recovery.