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Numerical determination of anomalies in multifrequency electrical impedance tomography

Published online by Cambridge University Press:  17 May 2018

HABIB AMMARI ,
FAOUZI TRIKI  and
CHUN-HSIANG TSOU
HABIB AMMARI
Affiliation:
Department of Mathematics, ETH Zürich, Rämistrasse 101, 8092 Zürich, Switzerland email: [email protected]
FAOUZI TRIKI
Affiliation:
Laboratoire Jean Kuntzmann, UMR CNRS 5224, Université Grenoble-Alpes, 700 Avenue Centrale, 38401 Saint-Martin-d'Hères, France email: [email protected]
CHUN-HSIANG TSOU
Affiliation:
Laboratoire Jean Kuntzmann, UMR CNRS 5224, Université Grenoble-Alpes, 700 Avenue Centrale, 38401 Saint-Martin-d'Hères, France email: [email protected]
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Abstract

The multifrequency electrical impedance tomography consists in retrieving the conductivity distribution of a sample by injecting a finite number of currents with multiple frequencies. In this paper, we consider the case where the conductivity distribution is piecewise constant, takes a constant value outside a single smooth anomaly, and a frequency dependent function inside the anomaly itself. Using an original spectral decomposition of the solution of the forward conductivity problem in terms of Poincaré variational eigenelements, we retrieve the Cauchy data corresponding to the extreme case of a perfect conductor, and the conductivity profile. We then reconstruct the anomaly from the Cauchy data. The numerical experiments are conducted using gradient descent optimization algorithms.

Keywords

Inverse problemsmultifrequency electric impedance tomographyanomalies reconstruction
Type
Papers
Information
European Journal of Applied Mathematics , Volume 30 , Issue 3 , June 2019 , pp. 481 - 504
Copyright
Copyright © Cambridge University Press 2018 

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Footnotes

This work has been partially supported by the LabEx PERSYVAL-Lab (ANR-11-LABX-0025-01).

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