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

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Journal Title
Journal ISSN
Volume Title
A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
Date
2021-03
Major/Subject
Mcode
Degree programme
Language
en
Pages
31
Series
Numerische Mathematik
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.
Description
Keywords
35R30, 35A35, 42A15, 42A10
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Citation
Garde , H & Hyvonen , N 2021 , ' Mimicking relative continuum measurements by electrode data in two-dimensional electrical impedance tomography ' , Numerische Mathematik , vol. 147 , no. 3 , pp. 579-609 . https://doi.org/10.1007/s00211-020-01170-8