Algorithm for image restoration based on variation and its convergence

A new algorithm for edge-preserving image restoration is presented in this paper. The variation based method can be effectively used in the process of non-convex optimization for solving the linear inverse problem. By analyzing the properties of regularization functions and the corresponding energy functional, an optimal expression of regularization function and a new energy functional with binary variables are introduced. Thus the non-convex optimization problem is transformed into a sequence of essentially convex one. The local optimal solution of no-convex optimization problem is then obtained by using a relaxation iterative algorithm. Such algorithm is shown to be globally convergent. Finally, the proposed method is tested on real and synthetic images.