We consider the problem of denoising images corrupted by a mixture of noise distributions, which is typical for instance in astronomy and microscopy applications. The resulting variational model is the joint MAP estimator of the likelihood function and combines single data fitting terms in a nonlinear infimal convolution fashion. A well-posedeness analysis in suitable function spaces is provided. For the efficient computation of the numerical solution, a SemiSmooth Newton method is used.

This presentation is part of Minisymposium “MS71 - Nonlinear and adaptive regularization for image restoration”
organized by: Claudio Estatico (University of Genoa) , Giuseppe Rodriguez (University of Cagliari) .

Authors:

Luca Calatroni (CMAP, École Polytechnique CNRS)

Carola-Bibiane Schönlieb (University of Cambridge)

Juan Carlos De Los Reyes (Escuela Politécnica Nacional)

Keywords:

bayesian methods, image reconstruction, inverse problems, partial differential equation models