Total variation with overlapping group sparsity for deblurring images under Cauchy noise

Abstract

Abstract The methods based on the total variation are effective for image deblurring and denoising, which can preserve edges and details of images. However, these methods usually produce some staircase effects. In order to alleviate the staircase effects, we propose a new convex model based on the total variation with overlapping group sparsity for recovering blurred images corrupted by Cauchy noise. Moreover, we develop an algorithm under the framework of the alternating direction method with multipliers, and use the majorization minimization to solve subproblems of the proposed algorithm. Numerical results illustrate that the proposed method outperforms other methods both in visual effects and quantitative measures, such as the peak signal-to-noise ratio and the structural similarity index.