Linearization-based Direct Reconstruction for Eit Using Triangular Zernike Decompositions

Antti Autio, Henrik Garde, Markus Hirvensalo, Nuutti Hyvonen

Research output: Contribution to journalArticleScientificpeer-review

Abstract

This work implements and numerically tests the direct reconstruction algorithm introduced in [Garde & Hyvönen, SIAM J. Math. Anal., 56, 3588-3604, 2024] for two-dimensional linearized electrical impedance tomography. Although the algorithm was originally designed for a linearized setting, we numerically demonstrate its functionality when the input data is the corresponding change in the current-to-voltage boundary operator. Both idealized continuum model and practical complete electrode model measurements are considered in the numerical studies, with the examined domain being either the unit disk or a convex polygon. Special attention is paid to regularizing the algorithm and its connections to the singular value decomposition of a truncated linearized forward map, as well as to the explicit triangular structures originating from the properties of the employed Zernike polynomial basis for the conductivity.
Original languageEnglish
Number of pages23
JournalInverse Problems and Imaging
DOIs
Publication statusE-pub ahead of print - Oct 2024
MoE publication typeA1 Journal article-refereed

Keywords

  • Electrical impedance tomography
  • Zernike polynomials
  • Direct reconstruction
  • Linearization
  • Singular value decomposition

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