A Scaled Gradient Projection Method for Constrained Image Deblurring

A class of scaled gradient projection methods for optimization problems with simple constraints is considered. These iterative algorithms can be useful in variational approaches to image deblurring that lead to minimize convex nonlinear functions subject to nonnegativity constraints and, in some cases, to an additional flux conservation constraint. A special gradient projection method is introduced that exploits effective scaling strategies and steplength updating rules, appropriately designed for improving the convergence rate. We give convergence results for this scheme and we evaluate its effectiveness by means of an extensive computational study on the minimization problems arising from the maximum likelihood approach to image deblurring. Comparisons with the standard expectation maximization algorithm and with other iterative regularization schemes are also reported to show the computational gain provided by the proposed method. AMS classification scheme numbers: 65K10, 65F22, 68U10 Submitted to: Inverse Problems