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 piecewis...

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Bibliographic Details
Published in:Numerische Mathematik 2018-03, Vol.138 (3), p.723-765
Main Authors: Hinze, Michael, Kaltenbacher, Barbara, Quyen, Tran Nhan Tam
Format: Article
Language:English
Subjects:
Electrical impedance
Electrical resistivity
Mathematical analysis
Mathematical and Computational Engineering
Mathematical and Computational Physics
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
Numerical Analysis
Numerical and Computational Physics
Regularization
Simulation
Theoretical
Tomography
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Summary: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.
ISSN:0029-599X
0945-3245
DOI:10.1007/s00211-017-0920-8