Gradient projection approaches for optimization problems in image deblurring and denoising

Gradient type methods are widely used approaches for nonlinear programming in image processing, due to their simplicity, low memory requirement and ability to provide medium-accurate solutions without excessive computational costs. In this work we discuss some improved gradient projection-methods for constrained optimization problems in image deblurring and denoising. Crucial feature of these approaches is the combination of special steplength rules and scaled gradient directions, appropriately designed to achieve a better convergence rate. Convergence results are given by exploiting monotone or nonmonotone line-search strategies along the feasible direction. The effectiveness of the algorithms is evaluated on the problems arising from the maximum likelihood approach to the deconvolution of images and from the edge-preserving removal of Poisson noise. Numerical results obtained by facing large scale problems involving images of several mega-pixels on graphics processors are also reported.