Mimicking relative continuum measurements by electrode data in two-dimensional electrical impedance tomography

Henrik Garde, Nuutti Hyvonen*

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

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Abstract

This paper introduces a constructive method for approximating relative continuum measurements in two-dimensional electrical impedance tomography based on data originating from either the point electrode model or the complete electrode model. The upper bounds for the corresponding approximation errors explicitly depend on the number (and size) of the employed electrodes as well as on the regularity of the continuum current that is mimicked. In particular, if the input current and the object boundary are infinitely smooth, the discrepancy associated with the point electrode model converges to zero faster than any negative power of the number of electrodes. The results are first proven for the unit disk via trigonometric interpolation and quadrature rules, and they are subsequently extended to more general domains with the help of conformal mappings.

Original languageEnglish
Number of pages31
JournalNumerische Mathematik
DOIs
Publication statusPublished - 15 Feb 2021
MoE publication typeA1 Journal article-refereed

Keywords

  • 35R30
  • 35A35
  • 42A15
  • 42A10

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