Smoothing Trust Region for Digital Image Restoration

The image restoration task is often modelled as an unconstrained minimization, which is composed of a quadratic data-fidelity term and a regularization term. Recently, nonsmooth regularization received significant attentions due to its excellent empirical performance on the presence of edges. To handle the nonsmoothness of the cost function, we propose a smoothing trust region algorithm in this paper. In order to make the new method more efficient and more suitable for big data situation, the Steihaug-CG algorithm is utilized to solve the trust region subproblem. New algorithm is compared with the Lucy-Richardson method. Numerical experiments on several images validate the effectiveness of the proposed method.