In this talk we will discuss the optimisation of a parametrised total variation regularisation approach in which the parameters correspond to weights in front of different total variation type regularisers and multiple convex discrepancy terms including L2, L1 and Kullback-Leibler discrepancies. Parameters in this model will be optimised with respect to a loss function that assesses the quality of the solution when compared to a training set of desirable solutions. The well-posedness, numerical solution and applications of this approach in image denoising will be discussed.

This presentation is part of Minisymposium “MS79 - From optimization to regularization in inverse problems and machine learning”
organized by: Silvia Villa (Politecnico di Milano) , Lorenzo Rosasco (University of Genoa, Istituto Italiano di Tecnologia; Massachusetts Institute of Technology) .

Authors:

Carola-Bibiane Schönlieb (University of Cambridge)

Juan Carlos De Los Reyes (Escuela Politécnica Nacional)

Luca Calatroni (CMAP, École Polytechnique CNRS)

Tuomo Valkonen (University of Liverpool)

Keywords: