Linearization-based direct reconstruction for EIT using triangular Zernike decompositions
<|reference_start|>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 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.<|reference_end|>
@article{autio2024linearization-based,
    title={Linearization-based direct reconstruction for EIT using triangular
  Zernike decompositions},
    author={Antti Autio, Henrik Garde, Markus Hirvensalo, Nuutti Hyv"onen},
    journal={arXiv preprint arXiv:2403.03320},
    year={2024},
    archivePrefix={arXiv},
    eprint={2403.03320},
    primaryClass={math.NA cs.NA}
}