In this paper we propose a new joint model for the reconstruction of tomography data under limited angle sampling regimes. In many applications of Tomography, e.g. Electron Microscopy and Mammography, physical limitations on acquisition lead to regions of data which cannot be sampled. Depending on the severity of the restriction, reconstructions can contain severe, characteristic, artefacts. Our model aims to address these artefacts by inpainting the missing data simultaneously with the reconstruction. Numerically, this problem naturally evolves to require the minimisation of a non-convex and non-smooth functional so we review recent work in this topic and extend results to fit an alternating (block) descent framework. We illustrate the effectiveness of this approach with numerical experiments on two synthetic datasets and one Electron Microscopy dataset.
@article{arxiv.1804.09991,
title = {Directional Sinogram Inpainting for Limited Angle Tomography},
author = {Robert Tovey and Martin Benning and Christoph Brune and Marinus J. Lagerwerf and Sean M. Collins and Rowan K. Leary and Paul A. Midgley and Carola-Bibiane Schoenlieb},
journal= {arXiv preprint arXiv:1804.09991},
year = {2018}
}
Comments
Revised manuscript accepted for publication in Inverse Problems