A simple primal–dual method for total variation image restoration

• A new simple primal–dual method is proposed.
• The method can get a closed-form solution in each iteration.
• O(1/N) convergence rate in the ergodic sense is established.
• The proposed method outperforms some state-of-the-art optimization algorithms.
• The algorithm is easy to extended to work on more general total variation image problems.

In this study we propose a simple primal–dual method for total variation minimization problems. A predictor–corrector scheme to the dual variable is used in our algorithms and convergence of the method is proved. We also show that the iterative scheme has O(1/N)O(1/N) convergence rate in the ergodic sense, where N denotes the iteration number. Numerical results including image deblurring and computerized tomography reconstruction demonstrate the efficient of the new algorithms.