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Series reversion for electrical impedance tomography with modeling errors

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  • Henrik Garde
  • Nuutti Hyvönen, Aalto University, Finland
  • Topi Kuutela, Aalto University, Finland

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.

Original languageEnglish
Article number085007
JournalInverse Problems
Number of pages29
Publication statusPublished - 2023

    Research areas

  • Bayesian inversion, Levenberg-Marquardt algorithm, electrical impedance tomography, mismodeling, series reversion, smoothened complete electrode model

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