  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.
