ALGORITHM FOR IMAGE RESTORATION BASED ON VARIATION AND ITS CONVERGENCE
基于变分的图像恢复算法及收敛性

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 non 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.