A primal-dual method with linear mapping for a saddle point problem in image deblurring

•A simple primal-dual method is presented for saddle point problem in image deblurring.•Each iteration consists of dual prediction, primal update and dual correction.•Convergence requirement on pairwise primal-dual stepsize is relaxed.•Simple proof is developed for O(1/N) convergence rate in ergodic sense.

In this paper, a simple primal-dual method named PDL is proposed for a convex concave saddle problem and applied to total variational image deblurring. Introduction of linear mapping on proximal term relaxes convergence requirement on pairwise primal-dual stepsize. Simple proof is presented for O(1/N) convergence rate in ergodic sense. Experiments show that performance of PDL is comparable with proximal PDHG (Zhu et al., 2010; Bonettini and Ruggiero, 2012) and PDCP (Chambolle and Pock, 2011) on Gaussian or Salt-Pepper noisy image deblurring.