2024/03/05 by Autio, Antti, Garde, Henrik, Hirvensalo, Markus +1 · 1 citation
#35R25 #35R30 #65N20 #65N21 #FOS: Mathematics #Numerical Analysis (math.NA)
paper · doi:10.48550/arxiv.2403.03320
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.