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

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Optimal depth-dependent distinguishability bounds for electrical impedance tomography in arbitrary dimension. / Garde, Henrik; Hyvönen, Nuutti.

I: SIAM Journal on Applied Mathematics, Bind 80, Nr. 1, 2020, s. 20-43.

Publikation: Bidrag til tidsskrift/Konferencebidrag i tidsskrift /Bidrag til avisTidsskriftartikelForskningpeer review

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Garde, Henrik ; Hyvönen, Nuutti. / Optimal depth-dependent distinguishability bounds for electrical impedance tomography in arbitrary dimension. I: SIAM Journal on Applied Mathematics. 2020 ; Bind 80, Nr. 1. s. 20-43.

Bibtex

@article{f2d70dfc19664a329fb007d60382b5fb,
title = "Optimal depth-dependent distinguishability bounds for electrical impedance tomography in arbitrary dimension",
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.",
keywords = "Depth dependence, Distinguishability, Electrical impedance tomography, Kelvin transformation",
author = "Henrik Garde and Nuutti Hyv{\"o}nen",
year = "2020",
doi = "10.1137/19M1258761",
language = "English",
volume = "80",
pages = "20--43",
journal = "SIAM Journal on Applied Mathematics",
issn = "0036-1399",
publisher = "Society for Industrial and Applied Mathematics",
number = "1",

}

RIS

TY - JOUR

T1 - Optimal depth-dependent distinguishability bounds for electrical impedance tomography in arbitrary dimension

AU - Garde, Henrik

AU - Hyvönen, Nuutti

PY - 2020

Y1 - 2020

N2 - 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.

AB - 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.

KW - Depth dependence

KW - Distinguishability

KW - Electrical impedance tomography

KW - Kelvin transformation

UR - http://www.scopus.com/inward/record.url?scp=85079596457&partnerID=8YFLogxK

U2 - 10.1137/19M1258761

DO - 10.1137/19M1258761

M3 - Journal article

VL - 80

SP - 20

EP - 43

JO - SIAM Journal on Applied Mathematics

JF - SIAM Journal on Applied Mathematics

SN - 0036-1399

IS - 1

ER -