Image restoration using total variation with overlapping group sparsity

Image restoration is one of the most fundamental issues in imaging science. Total variation regularization is widely used in image restoration problems for its capability to preserve edges. In the literature, however, it is also well known for producing staircase artifacts. In this work we extend the total variation with overlapping group sparsity, which we previously developed for one dimension signal processing, to image restoration. A convex cost function is given and an efficient algorithm is proposed for solving the corresponding minimization problem. In the experiments, we compare our method with several state-of-the-art methods. The results illustrate the efficiency and effectiveness of the proposed method in terms of PSNR and computing time.