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Incorporating structural prior information and sparsity into EIT using parallel level sets

Kolehmainen, V; Ehrhardt, MJ; Arridge, SR; (2019) Incorporating structural prior information and sparsity into EIT using parallel level sets. Inverse Problems and Imaging , 13 (2) pp. 285-307. 10.3934/ipi.2019015. Green open access

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Abstract

EIT is a non-linear ill-posed inverse problem which requires sophisticated regularisation techniques to achieve good results. In this paper we consider the use of structural information in the form of edge directions coming from an auxiliary image of the same object being reconstructed. In order to allow for cases where the auxiliary image does not provide complete information we consider in addition a sparsity regularization for the edges appearing in the EIT image. The combination of these approaches is conveniently described through the parallel level sets approach. We present an overview of previous methods for structural regularisation and then provide a variational setting for our approach and explain the numerical implementation. We present results on simulations and experimental data for different cases with accurate and inaccurate prior information. The results demonstrate that the structural prior information improves the reconstruction accuracy, even in cases when there is reasonable uncertainty in the prior about the location of the edges or only partial edge information is available.

Type: Article
Title: Incorporating structural prior information and sparsity into EIT using parallel level sets
Open access status: An open access version is available from UCL Discovery
DOI: 10.3934/ipi.2019015
Publisher version: http://doi.org/10.3934/ipi.2019015
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: Electrical impedance tomography, structural prior, computational inverse problem, regularization, finite element method.
UCL classification: UCL
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
UCL > Provost and Vice Provost Offices > UCL SLASH
UCL > Provost and Vice Provost Offices > UCL SLASH > Faculty of S&HS
URI: https://discovery.ucl.ac.uk/id/eprint/10073130
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