A new nonconvex approach for image restoration with Gamma noise

In this paper, a new total generalized variational(TGV) model for restoring images with multiplicative noise is proposed, which contains a nonconvex fidelity term and a TGV term. We use a difference of convex functions algorithm (DCA) to deal with the proposed model. For multiplicative noise removal, there exist many models and algorithms, most of which focus on convex approximation so that numerical algorithms with guaranteed convergence can be designed. Unlike these algorithms, we use the DCA algorithm to remove multiplicative noise. By numerical experiments, it is shown that the proposed approach leads to a better solution compared with the gradient projection algorithm for solving the classic multiplicative noise removal models. We prove that the sequence generated by the DCA algorithm converges to a stationary point, which satisfies the first order optimality condition. Finally, we demonstrate the performance of our whole scheme by numerical examples. A comparison with other methods is provided as well. Numerical results demonstrate that the proposed algorithm significantly outperforms some previous methods for multiplicative Gamma noise removal. (C) 2019 Elsevier Ltd. All rights reserved.