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At last, an explicit singular value decomposition for electrical impedance tomography
Abstract
We derive a diagonalization of the normal operator of the linearized electrical impedance tomography (EIT) problem on the disk in the case of a radially symmetric Schrödinger potential with Dirichlet-to-Neumann data. The diagonalization is achieved by transforming the normal operator to the adjacent interval finite Hilbert transform which has a known spectral theory including a commuting differential operator. The normal operator in this case is not compact and the spectrum continuous.
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BibTeX
@misc{lionheart2026last,
title = {{At last, an explicit singular value decomposition for electrical impedance tomography}},
author = {William R B Lionheart and Michael Pidcock and Cristiana Sebu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.35217},
eprint = {2610.35217},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.35217},
}
RIS
TY - UNPB
TI - At last, an explicit singular value decomposition for electrical impedance tomography
AU - William R B Lionheart
AU - Michael Pidcock
AU - Cristiana Sebu
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2610.35217
UR - https://arxiv.org/abs/2610.35217
AB - We derive a diagonalization of the normal operator of the linearized electrical impedance tomography (EIT) problem on the disk in the case of a radially symmetric Schrödinger potential with Dirichlet-to-Neumann data. The diagonalization is achieved by transforming the normal operator to the adjacent interval finite Hilbert transform which has a known spectral theory including a commuting differential operator. The normal operator in this case is not compact and the spectrum continuous.
ER -