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Journal of Inverse and Ill-posed Problems

Editor-in-Chief: Kabanikhin, Sergey I.


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1569-3945
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Volume 14, Issue 2

Issues

Towards a d-bar reconstruction method for three-dimensional EIT

H. Cornean
  • Department of Mathematical Sciences, Aalborg University, Fredrik Bajers Vej 7G, DK-9220 Aalborg, Denmark. E-mail:
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/ K. Knudsen
  • Department of Mathematical Sciences, Aalborg University, Fredrik Bajers Vej 7G, DK-9220 Aalborg, Denmark. E-mail:
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/ S. Siltanen
  • Department of Mathematics, Tampere University of Technology, PO Box 533, 33101 Tampere, Finland.
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Three-dimensional electrical impedance tomography (EIT) is considered. Both uniqueness proofs and theoretical reconstruction algorithms available for this problem rely on the use of exponentially growing solutions to the governing conductivity equation. The study of those solutions is continued here. It is shown that exponentially growing solutions exist for low complex frequencies without imposing any regularity assumption on the conductivity. Further, a reconstruction method for conductivities close to a constant is given. In this method the complex frequency is taken to zero instead of infinity. Since this approach involves only moderately oscillatory boundary data, it enables a new class of three-dimensional EIT algorithms, free from the usual high frequency instabilities.

About the article

Published Online:

Published in Print: 2006-04-01


Citation Information: Journal of Inverse and Ill-posed Problems jiip, Volume 14, Issue 2, Pages 111–134, ISSN (Online) 1569-3953, ISSN (Print) 0928-0219, DOI: https://doi.org/10.1515/156939406777571102.

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