The domain and property illusion of anomalous anisotropic electric conductivity

TL;DR

This paper explores the illusions created by anisotropic conductivities in electrical impedance tomography, revealing how domain size and properties of anomalies can be misrepresented due to mathematical equivalences.

Contribution

It demonstrates the illusion of anomaly size and property in anisotropic conductivities, extending the understanding of near-cloaking effects in EIT.

Findings

Anisotropic conductivities can produce identical boundary measurements.

The illusion affects both the perceived size and properties of anomalies.

The results have implications for the accuracy of EIT in anisotropic media.

Abstract

The unique determination of electrical conductivity is extensively studied for isotropic conductivity ever since Calderon's suggestion of the EIT (Electrical Impedance Tomography) problem. However, it is known that there are many anisotropic conductivities producing the same Dirichlet-to-Neumann map; moreover the anisotropic conductivities giving the same Dirichlet-to-Neumann map are classified using the equivalence relation with respect to the change of variables. The change of variable argument is applied to the theory of near-cloaking: We are under an illusion that the domain of anomaly is of a much smaller size than actually it is. For this paper, we considered not only the illusion of the domain of the anomaly, but also the illusion of the property of the anomaly when the background anisotropic conductivity is known.