Directional Sinogram Inpainting for Limited Angle Tomography

TL;DR

This paper introduces a joint inpainting and reconstruction model for limited angle tomography, effectively reducing artefacts caused by incomplete data in applications like Electron Microscopy and Mammography.

Contribution

It presents a novel non-convex, non-smooth functional minimization approach with an alternating descent framework for improved limited angle tomography reconstruction.

Findings

Effective artefact reduction demonstrated on synthetic datasets

Improved reconstruction quality in Electron Microscopy data

Extension of existing methods to a new alternating descent framework

Abstract

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.