Total Variation with Overlapping Group Sparsity for Image Deblurring under Impulse Noise

The total variation (TV) regularization method is an effective method for image deblurring in preserving edges. However, the TV based solutions usually have some staircase effects. In order to alleviate the staircase effects, we propose a new model for restoring blurred images under impulse noise. The model consists of an ℓ(1)-fidelity term and a TV with overlapping group sparsity (OGS) regularization term. Moreover, we impose a box constraint to the proposed model for getting more accurate solutions. The solving algorithm for our model is under the framework of the alternating direction method of multipliers (ADMM). We use an inner loop which is nested inside the majorization minimization (MM) iteration for the subproblem of the proposed method. Compared with other TV-based methods, numerical results illustrate that the proposed method can significantly improve the restoration quality, both in terms of peak signal-to-noise ratio (PSNR) and relative error (ReE).