Estimation of conductivity changes in a region of interest with electrical impedance tomography

Dong liu; Ville Kolehmainen; Samuli Siltanen; Anne-maria Laukkanen; Aku Seppänen

doi:10.3934/ipi.2015.9.211

Article Contents

2015, Volume 9, Issue 1: 211-229. Doi: 10.3934/ipi.2015.9.211

This issue Previous Article Near-field imaging of obstacles Next Article Sparse signals recovery from noisy measurements by orthogonal matching pursuit

Estimation of conductivity changes in a region of interest with electrical impedance tomography

1.
Department of Applied Physics, University of Eastern Finland, FIN-70211 Kuopio
2.
University of Eastern Finland, Department of Applied Physics, P.O.Box 1627, 70211 Kuopio
3.
University of Helsinki, Department of Mathematics and Statistics, FI-00014 Helsinki
4.
School of Education, University of Tampere, FIN-33014 Tampere
5.
Department of Applied Physics, University of Eastern Finland, 70211 Kuopio

Received: March 2014

Revised: September 2014

Published: February 2015

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Abstract

This paper proposes a novel approach to reconstruct changes in a target conductivity from electrical impedance tomography measurements. As in the conventional difference imaging, the reconstruction of the conductivity change is based on electrical potential measurements from the exterior boundary of the target before and after the change. In this paper, however, images of the conductivity before and after the change are reconstructed simultaneously based on the two data sets. The key feature of the approach is that the conductivity after the change is parameterized as a linear combination of the initial state and the change. This allows for modeling independently the spatial characteristics of the background conductivity and the change of the conductivity - by separate regularization functionals. The approach also allows in a straightforward way the restriction of the conductivity change to a localized region of interest inside the domain. While conventional difference imaging reconstruction is based on a global linearization of the observation model, the proposed approach amounts to solving a non-linear inverse problem. The feasibility of the proposed reconstruction method is tested experimentally and with a simulation which demonstrates a potential new medical application of electrical impedance tomography: imaging of vocal folds in voice loading studies.

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Mathematics Subject Classification: Primary: 65M32, 65N21, 92C55; Secondary: 65Z05, 65M60.

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