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.