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 extended proximal operators symmetric positive definite matrix D. Relaxing requirement on sizes, prove convergence proposed method. We also establish O(1/N) rate our in ergodic sense. Moreover, apply to solve TV- $$\hbox {L}_1$$ image deblurring problems. Numerical simulation results illustrate efficiency