Series reversion for electrical impedance tomography with modeling errors

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A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
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Inverse Problems, Volume 39, issue 8
This work extends the results of Garde and Hyvönen (2022 Math. Comput. 91 1925-1953) on series reversion for Calderón's problem to the case of realistic electrode measurements, with both the internal admittivity of the investigated body and the contact admittivity at the electrode-object interfaces treated as unknowns. The forward operator, sending the internal and contact admittivities to the linear electrode current-to-potential map, is first proven to be analytic. A reversion of the corresponding Taylor series yields a family of numerical methods of different orders for solving the inverse problem of electrical impedance tomography, with the possibility to employ different parametrizations for the unknown internal and boundary admittivities. The functionality and convergence of the methods is established only if the employed finite-dimensional parametrization of the unknowns allows the Fréchet derivative of the forward map to be injective, but we also heuristically extend the methods to more general settings by resorting to regularization motivated by Bayesian inversion. The performance of this regularized approach is tested via three-dimensional numerical examples based on simulated data. The effect of modeling errors related to electrode shapes and contact admittances is a focal point of the numerical studies.
Funding Information: The work of N H and T K was supported by the Academy of Finland (decision 336789) and Jane and Aatos Erkko Foundation via the project Electrical impedance tomography—a novel method for improved diagnostics of stroke. Publisher Copyright: © 2023 The Author(s). Published by IOP Publishing Ltd.
Bayesian inversion, electrical impedance tomography, Levenberg-Marquardt algorithm, mismodeling, series reversion, smoothened complete electrode model
Other note
Garde , H , Hyvönen , N & Kuutela , T 2023 , ' Series reversion for electrical impedance tomography with modeling errors ' , Inverse Problems , vol. 39 , no. 8 , 085007 , pp. 1-28 .