Preconditioned Three-Operator Splitting Algorithm with Applications to Image Restoration

Yuchao Tang, Meng Wen, Tieyong Zeng

Abstract: In this paper, we present primal-dual splitting algorithms for the convex minimization problem involving smooth functions with Lipschitzian gradient, finite sum of nonsmooth proximable functions, and linear composite functions. Many total variation-based image processing problems are special cases of such problems. The obtained primal-dual splitting algorithms are derived from a preconditioned three-operator splitting algorithm applied to primal-dual optimality conditions in a proper product space. The convergence of the proposed algorithms under appropriate assumptions on the parameters has been proved. Numerical experiments on a novel image restoration problem are presented to demonstrate the efficiency and effectiveness of the proposed algorithms.