Numerische Mathematik

, Volume 138, Issue 3, pp 723–765 | Cite as

Identifying conductivity in electrical impedance tomography with total variation regularization

  • Michael Hinze
  • Barbara Kaltenbacher
  • Tran Nhan Tam Quyen
Article
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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.

Keywords

Conductivity identification Electrical impedance tomography Total variation regularization Finite element method Neumann problem Dirichlet problem Ill-posed problems 

Mathematics Subject Classification

65N21 65N12 35J25 35R30 
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Notes

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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Copyright information

© Springer-Verlag GmbH Deutschland 2017

Authors and Affiliations

  • Michael Hinze
    • 1
  • Barbara Kaltenbacher
    • 2
  • Tran Nhan Tam Quyen
    • 1
  1. 1.University of HamburgHamburgGermany
  2. 2.Alpen-Adria-Universität KlagenfurtKlagenfurtAustria

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