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A direct D-bar method for partial boundary data electrical impedance tomography with a priori information

Alsaker, M; Hamilton, SJ; Hauptmann, A; (2017) A direct D-bar method for partial boundary data electrical impedance tomography with a priori information. Inverse Problems and Imaging , 11 (3) pp. 427-454. 10.3934/ipi.2017020. Green open access

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Abstract

Electrical Impedance Tomography (EIT) is a non-invasive imaging modality that uses surface electrical measurements to determine the internal conductivity of a body. The mathematical formulation of the EIT problem is a nonlinear and severely ill-posed inverse problem for which direct D-bar methods have proved useful in providing noise-robust conductivity reconstructions. Recent advances in D-bar methods allow for conductivity reconstructions using EIT measurement data from only part of the domain (e.g., a patient lying on their back could be imaged using only data gathered on the accessible part of the body). However, D-bar reconstructions suffer from a loss of sharp edges due to a nonlinear low-pass filtering of the measured data, and this problem becomes especially marked in the case of partial boundary data. Including a priori data directly into the D-bar solution method greatly enhances the spatial resolution, allowing for detection of underlying pathologies or defects, even with no assumption of their presence in the prior. This work combines partial data D-bar with a priori data, allowing for noise-robust conductivity reconstructions with greatly improved spatial resolution. The method is demonstrated to be effective on noisy simulated EIT measurement data simulating both medical and industrial imaging scenarios.

Type: Article
Title: A direct D-bar method for partial boundary data electrical impedance tomography with a priori information
Open access status: An open access version is available from UCL Discovery
DOI: 10.3934/ipi.2017020
Publisher version: https://doi.org/10.3934/ipi.2017020
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: Science & Technology, Physical Sciences, Mathematics, Applied, Physics, Mathematical, Mathematics, Physics, Electrical impedance tomography, partial boundary data, Neumann-to-Dirichlet map, D-bar method, a priori information, RESPIRATORY-DISTRESS-SYNDROME, INVERSE CONDUCTIVITY PROBLEM, TO-DIRICHLET MAP, DOMAIN TRUNCATION, ALGORITHM, RECONSTRUCTIONS, EIT, RESISTIVITIES, VENTILATION, CHEST
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/1575027
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