Identifying conductivity in electrical impedance tomography with total variation regularization

Identifying conductivity in electrical impedance tomography with total variation regularization In this paper we investigate the problem of identifying the conductivity in electrical impedance tomography from one boundary measurement. A variational method with total variation regularization is here proposed to tackle this problem. We discretize the PDE as well as the conductivity with piecewise linear, continuous finite elements. We prove the stability and convergence of this technique. For the numerical solution we propose a projected Armijo algorithm. Finally, a numerical experiment is presented to illustrate our theoretical results. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Numerische Mathematik Springer Journals

Identifying conductivity in electrical impedance tomography with total variation regularization

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Publisher
Springer Berlin Heidelberg
Copyright
Copyright © 2017 by Springer-Verlag GmbH Deutschland
Subject
Mathematics; Numerical Analysis; Mathematics, general; Theoretical, Mathematical and Computational Physics; Mathematical Methods in Physics; Numerical and Computational Physics, Simulation; Mathematical and Computational Engineering
ISSN
0029-599X
eISSN
0945-3245
D.O.I.
10.1007/s00211-017-0920-8
Publisher site
See Article on Publisher Site

Abstract

In this paper we investigate the problem of identifying the conductivity in electrical impedance tomography from one boundary measurement. A variational method with total variation regularization is here proposed to tackle this problem. We discretize the PDE as well as the conductivity with piecewise linear, continuous finite elements. We prove the stability and convergence of this technique. For the numerical solution we propose a projected Armijo algorithm. Finally, a numerical experiment is presented to illustrate our theoretical results.

Journal

Numerische MathematikSpringer Journals

Published: Sep 25, 2017

References

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