Linearization-based direct reconstruction for EIT using triangular Zernike decompositions

This work implements and numerically tests the direct reconstruction algorithm introduced in [Garde & Hyv\"onen, SIAM J. Math. Anal., 2024] for two-dimensional linearized electrical impedance tomography. Although the algorithm was originally designed for a linearized setting, we numerically...

Full description

Saved in:
Bibliographic Details
Published inarXiv.org
Main Authors Autio, Antti, Garde, Henrik, Hirvensalo, Markus, Hyvönen, Nuutti
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 05.03.2024
Subjects
Algorithms
Continuum modeling
Electrical impedance
Linearization
Mathematical analysis
Mathematical models
Reconstruction
Singular value decomposition
Zernike polynomials
Online AccessGet full text

Cover

More Information
Summary:This work implements and numerically tests the direct reconstruction algorithm introduced in [Garde & Hyv\"onen, SIAM J. Math. Anal., 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.
ISSN:2331-8422