Image denoising using combined higher order non-convex total variation with overlapping group sparsity

It is widely known that the total variation image restoration suffers from the stair casing artifacts which results in blocky restored images. In this paper, we address this problem by proposing a combined non-convex higher order total variation with overlapping group sparse regularizer. The hybrid scheme of both the overlapping group sparse and the non-convex higher order total variation for blocky artifact removal is complementary. The overlapping group sparse term tends to smoothen out blockiness in the restored image more globally, while the non-convex higher order term tends to smoothen parts that are more local to texture while preserving sharp edges. To solve the proposed image restoration model, we develop an iteratively re-weighted ℓ1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\ell _1$$\end{document} based alternating direction method of multipliers algorithm to deal with the constraints and subproblems. In this study, the images are degraded with different levels of Gaussian noise. A comparative analysis of the proposed method with the overlapping group sparse total variation, the Lysaker, Lundervold and Tai model, the total generalized variation and the non-convex higher order total variation, was carried out for image denoising. The results in terms of peak signal-to-noise ratio and structure similarity index measure show that the proposed method gave better performance than the compared algorithms.