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

Henrik Garde; Nuutti Hyvönen

doi:10.1137/19M1258761

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

Henrik Garde^*, Nuutti Hyvönen

^*Corresponding author af dette arbejde

Publikation: Bidrag til tidsskrift/Konferencebidrag i tidsskrift /Bidrag til avis › Tidsskriftartikel › Forskning › peer review

4 Citationer (Scopus)

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.

Originalsprog	Engelsk
Tidsskrift	SIAM Journal on Applied Mathematics
Vol/bind	80
Nummer	1
Sider (fra-til)	20-43
Antal sider	24
ISSN	0036-1399
DOI	https://doi.org/10.1137/19M1258761
Status	Udgivet - 2020
Udgivet eksternt	Ja

Adgang til dokumentet

10.1137/19M1258761

https://arxiv.org/abs/1904.12510

Citationsformater

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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.",

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KW - Distinguishability

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KW - Kelvin transformation

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