Linearized Calderón Problem: Reconstruction of Unbounded Perturbations in Three Dimensions

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A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä

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en

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14

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SIAM Journal on Applied Mathematics, Volume 85, issue 1, pp. 210-223

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Recently, an algorithm was given in Garde and Hyvönen [SIAM J. Math. Anal., 56 (2024), pp. 3588-3604] for exact direct reconstruction of any L2 perturbation from linearized data in the two-dimensional linearized Calderón problem. It was a simple forward substitution method based on a two-dimensional Zernike basis. We now consider the three-dimensional linearized Calderón problem in a ball and use a three-dimensional Zernike basis to obtain a method for exact direct reconstruction of any L3 perturbation from linearized data. The method is likewise a forward substitution, hence making it very efficient to numerically implement. Moreover, the three-dimensional method only makes use of a relatively small subset of boundary measurements for exact reconstruction compared to a full L2 basis of current densities.

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Publisher Copyright: © 2025 Society for Industrial and Applied Mathematics Publications. All rights reserved.

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Garde, H & Hirvensalo, M 2025, 'Linearized Calderón Problem: Reconstruction of Unbounded Perturbations in Three Dimensions', SIAM Journal on Applied Mathematics, vol. 85, no. 1, pp. 210-223. https://doi.org/10.1137/24M1649162