Monotonicity-Based Reconstruction of Extreme Inclusions in Electrical Impedance Tomography

Valentina Candiani, Jeremie Darde, Henrik Garde*, Nuutti Hyvönen

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

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Abstract

The monotonicity-based approach has become one of the fundamental methods for reconstructing inclusions in the inverse problem of electrical impedance tomography. Thus far, the method has not been proven to be able to handle extreme inclusions that correspond to some parts of the studied domain becoming either perfectly conducting or perfectly insulating. The main obstacle has arguably been establishing suitable monotonicity principles for the corresponding Neumann-to-Dirichlet boundary maps. In this work, we tackle this shortcoming by first giving a convergence result in the operator norm for the Neumann-to-Dirichlet map when the conductivity coefficient decays to zero and/or grows to infinity in some given parts of the domain. This allows passing the necessary monotonicity principles to the limiting case. Subsequently, we show how the monotonicity method generalizes to not only the definite case of reconstructing either perfectly conducting or perfectly insulating inclusions but also the indefinite case where the perturbed conductivity can take any values between, and including, zero and infinity.
Original languageEnglish
Pages (from-to)6234–6259
Number of pages26
JournalSIAM Journal on Mathematical Analysis
Volume52
Issue number6
DOIs
Publication statusPublished - 15 Dec 2020
MoE publication typeA1 Journal article-refereed

Keywords

  • electrical impedance tomography
  • perfectly insulating
  • perfectly conducting
  • monotonicity method

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