SGP-dec:A Scaled Gradient Projection method for2D and 3D images deconvolution

SGP-dec is a Matlab package for the deconvolution of 2D and 3D images corrupted by Poisson noise. Following amaximum likelihood approach, SGP-dec computes a deconvolved image by early stopping an iterative method for the minimization of the generalized Kullback-Lieibler divergence. The iterative minimization method implemented by SGP-dec is a Scaled Gradient Projection (SGP) algorithm that can be considered an acceleration of the Expectation Maximization method, also known as Richardson-Lucy method. The main feature of the SGP algorithm consists in the combination of non-expensivediagonally scaled gradient directions with adaptive Barzilai-Borwein steplength rules specially designed for thesedirections; global convergence properties are ensured by exploiting a line-search strategy (monotone or nonmonotone)along the feasible direction.The algorithm SGP is provided to be used as iterative regularization method; this means that a regularized reconstruction can be obtained by early stopping the SGP sequence. Several early stopping strategies can be selected, basedon different criteria: maximum number of iterations, distance of successive iterations or function values, discrepancyprinciple; the user must choose a stopping criterion and fixsuited values for the parameters involved by the chosen criterion.