Accelerated gradient methods for constrained image deblurring

In this paper we propose a special gradient projection method for the image deblurring problem, in the framework of the maximum likelihood approach. We present the method in a very general form and we give convergence results under standard assumptions. Then we consider the deblurring problem and the generality of the proposed algorithm allows us to add a energy conservation constraint to the maximum likelihood problem. In order to improve the convergence rate, we devise appropriate scaling strategies and steplength updating rules, especially designed for this application. The eectiveness of the method is evaluated by means of a computational study on astronomical images corrupted by Poisson noise. Comparisons with standard methods for image restoration, such as the expectation maximization algorithm, are also reported.