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Identifying conductivity in electrical impedance tomography with total variation regularization

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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.

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Acknowledgements

The authors M. Hinze, B. Kaltenbacher and T.N.T. Quyen would like to thank the referees and the editor for their valuable comments and suggestions which helped to improve our paper.

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Authors and Affiliations

  1. University of Hamburg, Bundesstraße 55, 20146, Hamburg, Germany

    Michael Hinze & Tran Nhan Tam Quyen

  2. Alpen-Adria-Universität Klagenfurt, Universitätsstraße 65-67, 9020, Klagenfurt, Austria

    Barbara Kaltenbacher

Authors
  1. Michael Hinze
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  2. Barbara Kaltenbacher
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  3. Tran Nhan Tam Quyen
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Corresponding author

Correspondence to Tran Nhan Tam Quyen.

Additional information

M. Hinze gratefully acknowledges support of the Lothar Collatz Center for Computing in Science at the University of Hamburg.

B. Kaltenbacher gratefully acknowledges support of the Austrian Wissenschaftsfonds through grant FWF I2271 entitled “Solving inverse problems without forward operators”.

T.N.T. Quyen gratefully acknowledges support of the Alexander von Humboldt-Foundation.

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Hinze, M., Kaltenbacher, B. & Quyen, T.N.T. Identifying conductivity in electrical impedance tomography with total variation regularization. Numer. Math. 138, 723–765 (2018). https://doi.org/10.1007/s00211-017-0920-8

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  • DOI: https://doi.org/10.1007/s00211-017-0920-8

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