  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 this paper, in order to alleviate the staircase
effect, we propose a new model for restoring blurred images with impulse noise.
The model consists of an $\ell_1$-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. An efficient and effective
algorithm is proposed to solve the model 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 methods, numerical results illustrate that
the proposed method, can significantly improve the restoration quality, both in
avoiding staircase effects and in terms of peak signal-to-noise ratio (PSNR)
and relative error (ReE).
