Proximal alternating minimization method for Poisson noise removal

In this paper, utilizing the quadratic penalty technique and adding a proximal term in one subproblem, we propose the proximal alternating minimization method for solving Poisson noise removal problem. For the fixed parameters, the convergence of proximal alternating algorithm is established under very mild conditions. In order to accelerate the proposed proximal algorithm, the variable stepsize, that is like Barzilai-Borwein stepsize, is applied to the proximal parameter. Compared with several state-of-the-arts algorithms, numerical results demonstrate the superiority of the new approach.