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Convergence and regularization for monotonicity-based shape reconstruction in electrical impedance tomography

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Convergence and regularization for monotonicity-based shape reconstruction in electrical impedance tomography. / Garde, Henrik; Staboulis, Stratos.

I: Numerische Mathematik, Bind 135, Nr. 4, 2017, s. 1221-1251.

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

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Garde, Henrik ; Staboulis, Stratos. / Convergence and regularization for monotonicity-based shape reconstruction in electrical impedance tomography. I: Numerische Mathematik. 2017 ; Bind 135, Nr. 4. s. 1221-1251.

Bibtex

@article{70d982e715c0429192b36393b89b1d01,
title = "Convergence and regularization for monotonicity-based shape reconstruction in electrical impedance tomography",
abstract = "The inverse problem of electrical impedance tomography is severely ill-posed, meaning that, only limited information about the conductivity can in practice be recovered from boundary measurements of electric current and voltage. Recently it was shown that a simple monotonicity property of the related Neumann-to-Dirichlet map can be used to characterize shapes of inhomogeneities in a known background conductivity. In this paper we formulate a monotonicity-based shape reconstruction scheme that applies to approximative measurement models, and regularizes against noise and modelling error. We demonstrate that for admissible choices of regularization parameters the inhomogeneities are detected, and under reasonable assumptions, asymptotically exactly characterized. Moreover, we rigorously associate this result with the complete electrode model, and describe how a computationally cheap monotonicity-based reconstruction algorithm can be implemented. Numerical reconstructions from both simulated and real-life measurement data are presented.",
keywords = "electrical impedance tomography, inverse problems, monotonicity method, regularization, complete electrode model ·, direct reconstruction methods",
author = "Henrik Garde and Stratos Staboulis",
year = "2017",
doi = "10.1007/s00211-016-0830-1",
language = "English",
volume = "135",
pages = "1221--1251",
journal = "Numerische Mathematik",
issn = "0029-599X",
publisher = "Springer",
number = "4",

}

RIS

TY - JOUR

T1 - Convergence and regularization for monotonicity-based shape reconstruction in electrical impedance tomography

AU - Garde, Henrik

AU - Staboulis, Stratos

PY - 2017

Y1 - 2017

N2 - The inverse problem of electrical impedance tomography is severely ill-posed, meaning that, only limited information about the conductivity can in practice be recovered from boundary measurements of electric current and voltage. Recently it was shown that a simple monotonicity property of the related Neumann-to-Dirichlet map can be used to characterize shapes of inhomogeneities in a known background conductivity. In this paper we formulate a monotonicity-based shape reconstruction scheme that applies to approximative measurement models, and regularizes against noise and modelling error. We demonstrate that for admissible choices of regularization parameters the inhomogeneities are detected, and under reasonable assumptions, asymptotically exactly characterized. Moreover, we rigorously associate this result with the complete electrode model, and describe how a computationally cheap monotonicity-based reconstruction algorithm can be implemented. Numerical reconstructions from both simulated and real-life measurement data are presented.

AB - The inverse problem of electrical impedance tomography is severely ill-posed, meaning that, only limited information about the conductivity can in practice be recovered from boundary measurements of electric current and voltage. Recently it was shown that a simple monotonicity property of the related Neumann-to-Dirichlet map can be used to characterize shapes of inhomogeneities in a known background conductivity. In this paper we formulate a monotonicity-based shape reconstruction scheme that applies to approximative measurement models, and regularizes against noise and modelling error. We demonstrate that for admissible choices of regularization parameters the inhomogeneities are detected, and under reasonable assumptions, asymptotically exactly characterized. Moreover, we rigorously associate this result with the complete electrode model, and describe how a computationally cheap monotonicity-based reconstruction algorithm can be implemented. Numerical reconstructions from both simulated and real-life measurement data are presented.

KW - electrical impedance tomography

KW - inverse problems

KW - monotonicity method

KW - regularization

KW - complete electrode model ·

KW - direct reconstruction methods

U2 - 10.1007/s00211-016-0830-1

DO - 10.1007/s00211-016-0830-1

M3 - Journal article

VL - 135

SP - 1221

EP - 1251

JO - Numerische Mathematik

JF - Numerische Mathematik

SN - 0029-599X

IS - 4

ER -