A Non-Convex Hybrid Overlapping Group Sparsity Model with Hyper-Laplacian Prior for Multiplicative Noise

Abstract

Multiplicative noise removal is a quite challenging problem in image denoising. In recent years, hyper-Laplacian prior information has been successfully introduced in the image denoising problem and significant denoising effects have been achieved. In this paper, we propose a new hybrid regularizer model for removing multiplicative noise. The proposed model consists of the non-convex higher-order total variation and overlapping group sparsity on a hyper-Laplacian prior regularizer. It combines the advantages of the non-convex regularization and the hybrid regularization, which may simultaneously preserve the fine-edge information and reduce the staircase effect at the same time. We develop an effective alternating minimization method for the proposed nonconvex model via an alternating direction method of multipliers framework, where the majorization–minimization algorithm and the iteratively reweighted algorithm are adopted to solve the corresponding subproblems. Numerical experiments show that the proposed model outperforms the most advanced model in terms of visual quality and certain image quality measurements.