A Nonsmooth Nonconvex Sparsity-Promoting Variational Approach for Deblurring Images Corrupted by Impulse Noise

We propose a new variational approach for the restoration of images simultaneously corrupted by blur and impulse noise. Promising results have been obtained by the ℓ1-TV variational model which contains a Total Variation (TV) regularization term and a nonsmooth convex ℓ1-norm data-fidelity term. We introduce a sparsity-promoting nonconvex data-fidelity term which performs better but makes the problem more difficult to handle. The main contribution of this paper is to develop a numerical algorithm based on the Alternating Direction Method of Multipliers (ADMM) strategy and on the use of proximal operators. Preliminary experiments are presented which strongly indicate that using nonconvex versus convex fidelities holds the potential for more accurate restorations at a modest computational extra-cost.