Ultrasound images speckle noise removal by nonconvex hybrid overlapping group sparsity model

In this paper, a novel hybrid variational model is proposed for speckle noise removal. This model contains the regularization term combined the nonconvex high-order total variation (HOTV) and overlapping group sparse total variation (OGSTV) and the data fidelity term depicted by a generalized Kullback–Leibler divergence. The proposed model inherits the advantages of nonconvex HOTV regularization and overlapping group sparse regularization and can more effectively preserve the edges and simultaneously eliminate staircase artifacts. Under the framework of alternating direction method of multipliers, we develop an efficient alternating minimization algorithm by using 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} algorithm, majorization–minimization algorithm, and Newton iteration algorithm to solve the corresponding iterative scheme. Numerical experiments show that the proposed model performs better in comparison with some state-of-the-art models in visual quality and certain image quality measurement.