An Iterative Algorithm for Sparse Recovery of Missing Image Samples Using a New Similarity Index

This paper investigates the problem of recovering missing samples using methods based on sparse representation adapted especially for image signals. Instead of $l_2$-norm or Mean Square Error (MSE), a new perceptual quality measure is used as the similarity criterion between the original and the reconstructed images. The proposed metric called Convex SIMilarity (CSIM) index is a modified version of the Structural SIMilarity (SSIM) index which despite its predecessor, is convex and uni-modal. We also propose an iterative sparse recovery method based on a constrained $l_1$-norm minimization problem involving CSIM as the fidelity criterion. This optimization problem which is adopted for missing sample recovery of images is efficiently solved via an algorithm based on Alternating Direction Method of Multipliers (ADMM). Simulation results show the performance of the new similarity index as well as the proposed algorithm for missing sample recovery of test images.