Image Recovery Using Total Variation Minimization on Compressive Sensing

Recently, total variation (TV) based minimization algorithms have obtained a considerable success in compressed sensing (CS) recovery for images, but the use of total variation is not able to recover the fine details and texture of images. In this paper, we propose an improved recovery algorithm by incorporating the local smoothness and nonlocal self-similarity constraints regularization in compressed sensing optimization problem, which help to preserve image properties. Furthermore, an efficient augmented Lagrangian algorithm is used to solve the above problem and optimize the solution. The proposed algorithm called total variation by augmented Lagrangian method (TV.ALM) is compared against Nesterov's algorithm (NESTA) and Two-step Iterative shrinkage/thresholding algorithm (TwIST) to evaluate their performance. Experimental results based on quality assessment such as peak signal-to-noise ratio, mean square error and structural similarity indicate that our algorithm TV.ALM achieves significant performance improvements in image recovery.