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
JF - SIAM Journal on Applied Mathematics
SN - 0036-1399
IS - 1
ER -