An improved first-order primal-dual algorithm with a new correction step

In this paper, we propose a new correction strategy for some first-order primal-dual algorithms arising from solving, e.g., total variation image restoration. With this strategy, we can prove the convergence of the algorithm under more flexible conditions than those proposed most recently. Some preliminary numerical results of image deblurring support that the new correction strategy can improve the numerical efficiency. Copyright Springer Science+Business Media New York 2013