Linearization-based direct reconstruction for EIT using triangular Zernike decompositions

Abstract

This work implements and numerically tests the direct reconstruction algorithm introduced in [Garde & Hyvönen, 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.

arXiv comment20 pages, 9 figures, 4 tables

References in corpus (3)

• Comparison of linear and non-linear monotononicity-based shape reconstruction using exact matrix characterizations
• Mimicking relative continuum measurements by electrode data in two-dimensional electrical impedance tomography
• Linearised Calderón problem: Reconstruction and Lipschitz stability for infinite-dimensional spaces of unbounded perturbations