An Efficient Primal-Dual Method for L1TV Image Restoration

Image restoration based on an `-data-fitting term and edge preserving total variation regularization is considered. The associated non-smooth energy minimization problem is handled by utilizing Fenchel-duality and dual regularization techniques. The latter guarantee uniqueness of the dual solution and an efficient way for reconstructing a primal solution, i.e. the restored image, from a dual solution. For solving the resulting primal-dual system, a semismooth Newton solver is proposed and its convergence is studied. The paper ends by a report on restoration results obtained by the new algorithm for saltand-pepper or random-valued impulse noise including blurring. A comparison with other methods is provided as well.