A new approach for Cauchy noise removal

In this paper, a new total generalized variational (TGV) model for restoring images with Cauchy noise is proposed, which contains a non-convex fidelity term and a TGV regularization term. In order to obtain a strictly convex model, we add an appropriate proximal term to the non-convex fidelity term. We prove that the solution of the proposed model exists and is unique. Due to the convexity of the proposed model and in order to get a convergent algorithm, we employ an alternating minimization algorithm to solve the proposed model. Finally, we demonstrate the performance of our scheme by numerical examples. Numerical results demonstrate that the proposed algorithm significantly outperforms some previous methods for Cauchy noise removal.