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Direct inversion from partial-boundary data in electrical impedance tomography

Hauptmann, A; Santacesaria, M; Siltanen, S; (2017) Direct inversion from partial-boundary data in electrical impedance tomography. Inverse Problems , 33 (2) , Article 025009. 10.1088/1361-6420/33/2/025009. Green open access

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Abstract

In electrical impedance tomography (EIT) one wants to image the conductivity distribution of a body from current and voltage measurements carried out on its boundary. In this paper we consider the underlying mathematical model, the inverse conductivity problem, in two dimensions and under the realistic assumption that only a part of the boundary is accessible to measurements. In this framework our data are modeled as a partial Neumann-to-Dirichlet map (ND map). We compare this data to the full-boundary ND map and prove that the error depends linearly on the size of the missing part of the boundary. The same linear dependence is further proved for the difference of the reconstructed conductivities—from partial and full boundary data. The reconstruction is based on a truncated and linearized D-bar method. Auxiliary results include an extrapolation method to estimate the full-boundary data from the measured one, an approximation of the complex geometrical optics solutions computed directly from the ND map as well as an approximate scattering transform for reconstructing the conductivity. Numerical verification of the convergence results and reconstructions are presented for simulated test cases.

Type: Article
Title: Direct inversion from partial-boundary data in electrical impedance tomography
Open access status: An open access version is available from UCL Discovery
DOI: 10.1088/1361-6420/33/2/025009
Publisher version: https://doi.org/10.1088/1361-6420/33/2/025009
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: inverse conductivity problem, electrical impedance tomography, Neumann-to-Dirichlet map, partial-boundary data, D-bar method
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/10052056
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