We consider optimization problems modeling image restoration from Poisson data. The objective function is the generalized Kullback-Leibler (KL) divergence plus a TV regularizer; nonnegativity and photon-flux conservation constraints are imposed. We propose an iterative procedure where quadratic problems, obtained by classical approximation of KL and iteratively reweighted least-squares (IRLS) approximation of TV, are solved inexactly by a two-phase gradient projection method. A convergence proof of our procedure and numerical experiments showing its effectiveness are presented.

This presentation is part of Minisymposium “MS10 - Advanced optimization methods for image processing (2 parts)”
organized by: Marco Prato (University of Modena and Reggio Emilia) , Ignace Loris (Université Libre de Bruxelles) .

Authors:

Daniela di Serafino (University of Campania "L. Vanvitelli")

Germana Landi (University of Bologna)

Marco Viola (University of Rome “La Sapienza”)

Keywords:

image reconstruction, iterative reweighting approach, nonlinear optimization, poisson noise, tv regularization, two-phase gradient projection method