Nonmonotone and Monotone Active Set Methods for Image Restoration

Active set methods based on the augmented Lagrangian smoothing of nondiier-entiable optimization problems that arise in image restoration are discussed. One-dimensional image restoration problem and two diierent formulations for two-dimensional image restoration problem are given. Both nonmonotone and monotone active set algorithms are described and nite step convergence of the algorithms is considered. New, direct way for solving the constrained optimization problem that appears in the inner iteration of the monotone algorithms is presented. Several numerical examples are included.