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

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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
Pages (from-to)20-43
Number of pages24
JournalSIAM Journal on Applied Mathematics
Volume80
Issue number1
DOIs
Publication statusPublished - 1 Jan 2020
MoE publication typeA1 Journal article-refereed

Keywords

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

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