The limited angle problem in Computed Tomography is unavoidable and results in severely ill-posed inverse problems with strong reconstruction artefacts. We propose a joint approach which simultaneously refines our estimate for the missing data and the desired reconstruction to minimise these artefacts. Such a model naturally leads us to consider non-linear constraints and non-convex, non-smooth optimisation. We shall review and extend recent results in this area for practical implementation.

This presentation is part of Minisymposium “MS62 - Imaging models with non-linear constraints (2 parts)”
organized by: Tuomo Valkonen (University of Liverpool) , Juan Carlos De Los Reyes (Escuela Politécnica Nacional) .

Authors:

Rob Tovey (University of Cambridge)

Rien Lagerwerf (Centrum Wiskunde & Informatica)

Christoph Brune (University of Twente)

Martin Benning (University of Cambridge)

Carola-Bibiane Schönlieb (University of Cambridge)

Keywords:

computed tomography, image inpainting, image reconstruction, inverse problems, nonconvex optimization, nonlinear optimization