Optimal depth-dependent distinguishability bounds for electrical impedance tomography in arbitrary dimension

Henrik Garde*, Nuutti Hyvönen

*Corresponding author for this work

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

Abstract

The inverse problem of electrical impedance tomography is severely ill-posed. In particular, the resolution of images produced by impedance tomography deteriorates as the distance from the measurement boundary increases. Such depth dependence can be quantified by the concept of distinguishability of inclusions. This paper considers the distinguishability of perfectly conducting ball inclusions inside a unit ball domain, extending and improving known two-dimensional results to an arbitrary dimension d ≥ 2 with the help of Kelvin transformations. The obtained depth-dependent distinguishability bounds are also proven to be optimal.

Original languageEnglish
JournalSIAM Journal on Applied Mathematics
Volume80
Issue1
Pages (from-to)20-43
Number of pages24
ISSN0036-1399
DOIs
Publication statusPublished - 2020
Externally publishedYes

Keywords

  • Depth dependence
  • Distinguishability
  • Electrical impedance tomography
  • Kelvin transformation

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