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

Aalborg University

Research output: Contribution to journal › Article › Scientific › peer-review

6 Citations (Web of Science)

172 Downloads (Pure)

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 language	English
Pages (from-to)	20-43
Number of pages	24
Journal	SIAM Journal on Applied Mathematics
Volume	80
Issue number	1
DOIs	https://doi.org/10.1137/19M1258761
Publication status	Published - 1 Jan 2020
MoE publication type	A1 Journal article-refereed

Funding

\ast Received by the editors April 29, 2019; accepted for publication (in revised form) October 3, 2019; published electronically January 2, 2020. https://doi.org/10.1137/19M1258761 Funding: This work was supported by the Academy of Finland through grant 312124 and by the Aalto Science Institute (AScI). \dagger Department of Mathematical Sciences, Aalborg University, Skjernvej 4A, 9220 Aalborg, Denmark ([email protected]). \ddagger Department of Mathematics and Systems Analysis, Aalto University, P.O. Box 11100, 02150 Espoo, Finland ([email protected]).

Keywords

Depth dependence
Distinguishability
Electrical impedance tomography
Kelvin transformation

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10.1137/19M1258761

Garde_Optimal.19m1258761Final published version, 564 KB

Cite this

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

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Centre of Excellence of Inverse Modelling and Imaging

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

Abstract

Funding

Keywords

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Other files and links

Fingerprint

Projects

Centre of Excellence of Inverse Modelling and Imaging

Cite this