Image restoration using overlapping group sparsity on hyper-Laplacian prior of image gradient

Abstract Due to the ill-posed nature of image restoration, seeking a meaningful image prior is still a great challenge in the field of image processing. The total variation with overlapping group sparsity (OGS-TV) has been successfully applied for image denoising/deblurring. In this paper, we further study the overlapping group sparsity of the image gradient. The sparsity is measured by the l q quasi-norm ( 0 q 1 ). The proposed regularizer comes down to the well-known hyper-Laplacian prior if the overlapping group size is 1. Although it seems to be a simple extensive study compared with the previous works, its regularization capability and corresponding mathematical problems are still in demand for imaging science. To solve the non-convex and non-smooth minimization problem, we use the alternating direction method of multipliers as the main algorithm framework. The difficult inner subproblem is tackled by the majorization-minimization method with the sophisticatedly derived majorizer. We carry out some numerical experiments to demonstrate the effectiveness of the proposed regularizer in terms of PSNR and SSIM values.