A direct reconstruction algorithm for the anisotropic inverse conductivity problem based on Calder\'on's method in the plane
Numerical Analysis
2020-07-20 v1 Numerical Analysis
Analysis of PDEs
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.
Cite
@article{arxiv.2007.08777,
title = {A direct reconstruction algorithm for the anisotropic inverse conductivity problem based on Calder\'on's method in the plane},
author = {Rashmi Murthy and Yi-Hsuan Lin and Kwancheol Shin and Jennifer L. Mueller},
journal= {arXiv preprint arXiv:2007.08777},
year = {2020}
}