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

N. Hyvönen, V. Kaarnioja, L. Mustonen, S. Staboulis

Research output: Contribution to journalArticleScientificpeer-review

5 Citations (Scopus)
114 Downloads (Pure)

Abstract

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.

Original languageEnglish
Pages (from-to)202-223
Number of pages22
JournalSIAM Journal on Applied Mathematics
Volume77
Issue number1
DOIs
Publication statusPublished - 2017
MoE publication typeA1 Journal article-refereed

Keywords

  • Bayesian inversion
  • Complete electrode model
  • Electrical impedance tomography
  • Inaccurate measurement model
  • Polynomial collocation
  • Uncertainty quantification

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