An inexact primal–dual method with correction step for a saddle point problem in image debluring

Abstract

In this paper, we present an inexact primal–dual method with correction step for a saddle point problem by introducing the notations of inexact extended proximal operators with symmetric positive definite matrix D. Relaxing requirement on primal–dual step sizes, we prove the convergence of the proposed method. We also establish the O(1/N) convergence rate of our method in the ergodic sense. Moreover, we apply our method to solve TV-\(\hbox {L}_1\) image deblurring problems. Numerical simulation results illustrate the efficiency of our method.