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arXiv · 2403.03320

Linearization-based direct reconstruction for EIT using triangular Zernike decompositions

Antti Autio·Henrik Garde·Markus Hirvensalo·Nuutti Hyvönen
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Abstract

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.

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Antti Autio, Henrik Garde, Markus Hirvensalo, Nuutti Hyvönen. 2024-03-05. Linearization-based direct reconstruction for EIT using triangular Zernike decompositions. https://doi.org/10.3934/ipi.2024040

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