A modified Chambolle-Pock primal-dual algorithm for Poisson noise removal

In this paper, we study the Poisson noise removal problem with total variation regularization term. Using the dual formulation of total variation and Lagrange dual, we formulate the problem as a new constrained minimax problem. Then, a modified Chambolle-Pock first-order primal-dual algorithm is developed to compute the saddle point of the minimax problem. The main idea of this paper is using different step size for different primal (dual) variables updating. Moreover, the convergence of the proposed method is also established under mild conditions. Numerical comparisons between new approach and several state-of-the-art algorithms are shown to demonstrate the effectiveness of the new algorithm.