Linearised Calder\'on problem: Reconstruction of unbounded perturbations in 3D
<|reference_start|>Linearised Calder\'on problem: Reconstruction of unbounded perturbations in 3D: Recently an algorithm was given in [Garde & Hyv\"onen, SIAM J. Math. Anal., 2024] for exact direct reconstruction of any $L^2$ perturbation from linearised data in the two-dimensional linearised Calder\'on problem. It was a simple forward substitution method based on a 2D Zernike basis. We now consider the three-dimensional linearised Calder\'on problem in a ball, and use a 3D Zernike basis to obtain a method for exact direct reconstruction of any $L^3$ perturbation from linearised data. The method is likewise a forward substitution, hence making it very efficient to numerically implement. Moreover, the 3D method only makes use of a relatively small subset of boundary measurements for exact reconstruction, compared to a full $L^2$ basis of current densities.<|reference_end|>
@article{garde2024linearised,
    title={Linearised Calder\'on problem: Reconstruction of unbounded perturbations
  in 3D},
    author={Henrik Garde and Markus Hirvensalo},
    journal={arXiv preprint arXiv:2403.16588},
    year={2024},
    archivePrefix={arXiv},
    eprint={2403.16588},
    primaryClass={math.AP cs.NA math.NA}
}