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arXiv · 2007.08777

A direct reconstruction algorithm for the anisotropic inverse conductivity problem based on Calder\'on's method in the plane

Rashmi Murthy·Yi-Hsuan Lin·Kwancheol Shin·Jennifer L. Mueller
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Abstract

A direct reconstruction algorithm based on Calder\'on's linearization method for the reconstruction of isotropic conductivities is proposed for anisotropic conductivities in two-dimensions. To overcome the non-uniqueness of the anisotropic inverse conductivity problem, the entries of the unperturbed anisotropic tensors are assumed known \emph{a priori}, and it remains to reconstruct the multiplicative scalar field. The quasi-conformal map in the plane facilitates the Calder\'on-based approach for anisotropic conductivities. The method is demonstrated on discontinuous radially symmetric conductivities of high and low contrast.

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Rashmi Murthy, Yi-Hsuan Lin, Kwancheol Shin, Jennifer L. Mueller. 2020-07-17. A direct reconstruction algorithm for the anisotropic inverse conductivity problem based on Calder\'on's method in the plane. https://arxiv.org/abs/2007.08777

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