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Monotonicity-based reconstruction of extreme inclusions in electrical impedance tomography

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Standard

Monotonicity-based reconstruction of extreme inclusions in electrical impedance tomography. / Candiani, Valentina; Dardé, Jérémi; Garde, Henrik; Hyvönen, Nuutti.

I: SIAM Journal on Mathematical Analysis, Bind 52, Nr. 6, 12.2020, s. 6234–6259.

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

Harvard

Candiani, V, Dardé, J, Garde, H & Hyvönen, N 2020, 'Monotonicity-based reconstruction of extreme inclusions in electrical impedance tomography', SIAM Journal on Mathematical Analysis, bind 52, nr. 6, s. 6234–6259. https://doi.org/10.1137/19M1299219

APA

Candiani, V., Dardé, J., Garde, H., & Hyvönen, N. (2020). Monotonicity-based reconstruction of extreme inclusions in electrical impedance tomography. SIAM Journal on Mathematical Analysis, 52(6), 6234–6259. https://doi.org/10.1137/19M1299219

CBE

Candiani V, Dardé J, Garde H, Hyvönen N. 2020. Monotonicity-based reconstruction of extreme inclusions in electrical impedance tomography. SIAM Journal on Mathematical Analysis. 52(6):6234–6259. https://doi.org/10.1137/19M1299219

MLA

Candiani, Valentina o.a.. "Monotonicity-based reconstruction of extreme inclusions in electrical impedance tomography". SIAM Journal on Mathematical Analysis. 2020, 52(6). 6234–6259. https://doi.org/10.1137/19M1299219

Vancouver

Candiani V, Dardé J, Garde H, Hyvönen N. Monotonicity-based reconstruction of extreme inclusions in electrical impedance tomography. SIAM Journal on Mathematical Analysis. 2020 dec;52(6):6234–6259. https://doi.org/10.1137/19M1299219

Author

Candiani, Valentina ; Dardé, Jérémi ; Garde, Henrik ; Hyvönen, Nuutti. / Monotonicity-based reconstruction of extreme inclusions in electrical impedance tomography. I: SIAM Journal on Mathematical Analysis. 2020 ; Bind 52, Nr. 6. s. 6234–6259.

Bibtex

@article{38d2e3ed0f6b4185a162fa38359aa701,
title = "Monotonicity-based reconstruction of extreme inclusions in electrical impedance tomography",
abstract = "The monotonicity-based approach has become one of the fundamental methods for reconstructing inclusions in the inverse problem of electrical impedance tomography. Thus far the method has not been proven to be able to handle extreme inclusions that correspond to some parts of the studied domain becoming either perfectly conducting or perfectly insulating. The main obstacle has arguably been establishing suitable monotonicity principles for the corresponding Neumann-to-Dirichlet boundary maps. In this work, we tackle this shortcoming by first giving a convergence result in the operator norm for the Neumann-to-Dirichlet map when the conductivity coefficient decays to zero and/or grows to infinity in some given parts of the domain. This allows passing the necessary monotonicity principles to the limiting case. Subsequently, we show how the monotonicity method generalizes to the definite case of reconstructing either perfectly conducting or perfectly insulating inclusions, as well as to the indefinite case where the perturbed conductivity can take any values between, and including, zero and infinity.",
author = "Valentina Candiani and J{\'e}r{\'e}mi Dard{\'e} and Henrik Garde and Nuutti Hyv{\"o}nen",
year = "2020",
month = dec,
doi = "10.1137/19M1299219",
language = "English",
volume = "52",
pages = "6234–6259",
journal = "SIAM Journal on Mathematical Analysis",
issn = "0036-1410",
publisher = "Society for Industrial and Applied Mathematics",
number = "6",

}

RIS

TY - JOUR

T1 - Monotonicity-based reconstruction of extreme inclusions in electrical impedance tomography

AU - Candiani, Valentina

AU - Dardé, Jérémi

AU - Garde, Henrik

AU - Hyvönen, Nuutti

PY - 2020/12

Y1 - 2020/12

N2 - The monotonicity-based approach has become one of the fundamental methods for reconstructing inclusions in the inverse problem of electrical impedance tomography. Thus far the method has not been proven to be able to handle extreme inclusions that correspond to some parts of the studied domain becoming either perfectly conducting or perfectly insulating. The main obstacle has arguably been establishing suitable monotonicity principles for the corresponding Neumann-to-Dirichlet boundary maps. In this work, we tackle this shortcoming by first giving a convergence result in the operator norm for the Neumann-to-Dirichlet map when the conductivity coefficient decays to zero and/or grows to infinity in some given parts of the domain. This allows passing the necessary monotonicity principles to the limiting case. Subsequently, we show how the monotonicity method generalizes to the definite case of reconstructing either perfectly conducting or perfectly insulating inclusions, as well as to the indefinite case where the perturbed conductivity can take any values between, and including, zero and infinity.

AB - The monotonicity-based approach has become one of the fundamental methods for reconstructing inclusions in the inverse problem of electrical impedance tomography. Thus far the method has not been proven to be able to handle extreme inclusions that correspond to some parts of the studied domain becoming either perfectly conducting or perfectly insulating. The main obstacle has arguably been establishing suitable monotonicity principles for the corresponding Neumann-to-Dirichlet boundary maps. In this work, we tackle this shortcoming by first giving a convergence result in the operator norm for the Neumann-to-Dirichlet map when the conductivity coefficient decays to zero and/or grows to infinity in some given parts of the domain. This allows passing the necessary monotonicity principles to the limiting case. Subsequently, we show how the monotonicity method generalizes to the definite case of reconstructing either perfectly conducting or perfectly insulating inclusions, as well as to the indefinite case where the perturbed conductivity can take any values between, and including, zero and infinity.

U2 - 10.1137/19M1299219

DO - 10.1137/19M1299219

M3 - Journal article

VL - 52

SP - 6234

EP - 6259

JO - SIAM Journal on Mathematical Analysis

JF - SIAM Journal on Mathematical Analysis

SN - 0036-1410

IS - 6

ER -