TV-based Poisson image restoration by IRLS and gradient projection methodsMS10

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) .

Daniela di Serafino (University of Campania "L. Vanvitelli")
Germana Landi (University of Bologna)
Marco Viola (University of Rome “La Sapienza”)
image reconstruction, iterative reweighting approach, nonlinear optimization, poisson noise, tv regularization, two-phase gradient projection method