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A variational reconstruction method for undersampled dynamic x-ray tomography based on physical motion models

Burger, M; Dirks, H; Frerking, L; Hauptmann, A; Helin, T; Siltanen, S; (2017) A variational reconstruction method for undersampled dynamic x-ray tomography based on physical motion models. Inverse Problems , 33 (12) , Article 124008. 10.1088/1361-6420/aa99cf. Green open access

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Abstract

In this paper we study the reconstruction of moving object densities from undersampled dynamic x-ray tomography in two dimensions. A particular motivation of this study is to use realistic measurement protocols for practical applications, i.e. we do not assume to have a full Radon transform in each time step, but only projections in few angular directions. This restriction enforces a space-time reconstruction, which we perform by incorporating physical motion models and regularization of motion vectors in a variational framework. The methodology of optical flow, which is one of the most common methods to estimate motion between two images, is utilized to formulate a joint variational model for reconstruction and motion estimation. We provide a basic mathematical analysis of the forward model and the variational model for the image reconstruction. Moreover, we discuss the efficient numerical minimization based on alternating minimizations between images and motion vectors. A variety of results are presented for simulated and real measurement data with different sampling strategy. A key observation is that random sampling combined with our model allows reconstructions of similar amount of measurements and quality as a single static reconstruction.

Type: Article
Title: A variational reconstruction method for undersampled dynamic x-ray tomography based on physical motion models
Open access status: An open access version is available from UCL Discovery
DOI: 10.1088/1361-6420/aa99cf
Publisher version: https://doi.org/10.1088/1361-6420/aa99cf
Language: English
Additional information: This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions.
Keywords: dynamic inverse problems, variational reconstruction, undersampled data, x-ray tomography, motion estimation
UCL classification: UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Computer Science
URI: http://discovery.ucl.ac.uk/id/eprint/10045241
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