Reconstruction of piecewise constant layered conductivities in electrical impedance tomography

Henrik Garde*

*Corresponding author for this work

Research output: Contribution to journal/Conference contribution in journal/Contribution to newspaperJournal articleResearchpeer-review

Abstract

This work presents a new constructive uniqueness proof for Calderón’s inverse problem of electrical impedance tomography, subject to local Cauchy data, for a large class of piecewise constant conductivities that we call piecewise constant layered conductivities (PCLC). The resulting reconstruction method only relies on the physically intuitive monotonicity principles of the local Neumann-to-Dirichlet map, and therefore the method lends itself well to efficient numerical implementation and generalization to electrode models. Several direct reconstruction methods exist for the related problem of inclusion detection, however they share the property that “holes in inclusions” or “inclusions-within-inclusions” cannot be determined. One such method is the monotonicity method of Harrach, Seo, and Ullrich, and in fact the method presented here is a modified variant of the monotonicity method which overcomes this problem. More precisely, the presented method abuses that a PCLC type conductivity can be decomposed into nested layers of positive and/or negative perturbations that, layer-by-layer, can be determined via the monotonicity method. The conductivity values on each layer are found via basic one-dimensional optimization problems constrained by monotonicity relations.

Original languageEnglish
JournalCommunications in Partial Differential Equations
Volume45
Issue9
Pages (from-to)1118-1133
Number of pages16
ISSN0360-5302
DOIs
Publication statusPublished - 2020
Externally publishedYes

Keywords

  • Electrical impedance tomography
  • monotonicity principle
  • partial data reconstruction
  • piecewise constant coefficient

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