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

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- L_1 image deblurring problems. Numerical simulation results illustrate the efficiency of our method.