At last, an explicit singular value decomposition for electrical impedance tomography

William R B Lionheart; Michael Pidcock; Cristiana Sebu

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arXiv · 2610.35217

At last, an explicit singular value decomposition for electrical impedance tomography

William R B Lionheart·Michael Pidcock·Cristiana Sebu

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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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William R B Lionheart, Michael Pidcock, Cristiana Sebu. 2026-10-26. At last, an explicit singular value decomposition for electrical impedance tomography. https://arxiv.org/abs/2610.35217

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