# Polynomial collocation for handling an inaccurately known measurement configuration in electrical impedance tomography

Research output: Scientific - peer-review › Article

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**Polynomial collocation for handling an inaccurately known measurement configuration in electrical impedance tomography.** / Hyvönen, N.; Kaarnioja, V.; Mustonen, L.; Staboulis, S.

Research output: Scientific - peer-review › Article

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*SIAM JOURNAL ON APPLIED MATHEMATICS*, vol 77, no. 1, pp. 202-223. DOI: 10.1137/16M1068888

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*SIAM JOURNAL ON APPLIED MATHEMATICS*,

*77*(1), 202-223. DOI: 10.1137/16M1068888

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TY - JOUR

T1 - Polynomial collocation for handling an inaccurately known measurement configuration in electrical impedance tomography

AU - Hyvönen,N.

AU - Kaarnioja,V.

AU - Mustonen,L.

AU - Staboulis,S.

PY - 2017

Y1 - 2017

N2 - The objective of electrical impedance tomography is to reconstruct the internal conductivity of a physical body based on measurements of current and potential at a finite number of electrodes attached to its boundary. Although the conductivity is the quantity of main interest in impedance tomography, a real-world measurement configuration includes other unknown parameters as well: The information on the contact resistances, electrode positions, and body shape is almost always incomplete. In this work, the dependence of the electrode measurements on all aforementioned model properties is parametrized via polynomial collocation. The availability of such a parametrization enables efficient simultaneous reconstruction of the conductivity and other unknowns by a Newton-type output least squares algorithm, which is demonstrated by two-dimensional numerical experiments based on both noisy simulated data and experimental data from two water tanks.

AB - The objective of electrical impedance tomography is to reconstruct the internal conductivity of a physical body based on measurements of current and potential at a finite number of electrodes attached to its boundary. Although the conductivity is the quantity of main interest in impedance tomography, a real-world measurement configuration includes other unknown parameters as well: The information on the contact resistances, electrode positions, and body shape is almost always incomplete. In this work, the dependence of the electrode measurements on all aforementioned model properties is parametrized via polynomial collocation. The availability of such a parametrization enables efficient simultaneous reconstruction of the conductivity and other unknowns by a Newton-type output least squares algorithm, which is demonstrated by two-dimensional numerical experiments based on both noisy simulated data and experimental data from two water tanks.

KW - Bayesian inversion

KW - Complete electrode model

KW - Electrical impedance tomography

KW - Inaccurate measurement model

KW - Polynomial collocation

KW - Uncertainty quantification

UR - http://www.scopus.com/inward/record.url?scp=85014451887&partnerID=8YFLogxK

U2 - 10.1137/16M1068888

DO - 10.1137/16M1068888

M3 - Article

VL - 77

SP - 202

EP - 223

JO - SIAM JOURNAL ON APPLIED MATHEMATICS

T2 - SIAM JOURNAL ON APPLIED MATHEMATICS

JF - SIAM JOURNAL ON APPLIED MATHEMATICS

SN - 0036-1399

IS - 1

ER -

ID: 11326229