Probabilistic interpretation of electrical impedance tomography

TL;DR

This paper provides a probabilistic framework for understanding electrical impedance tomography, including forward and inverse problems, using advanced mathematical tools like Dirichlet spaces and diffusion processes, applicable to anisotropic conductivities.

Contribution

It introduces a novel probabilistic interpretation of both the forward and inverse problems in electrical impedance tomography, extending to anisotropic and measurable conductivities.

Findings

Derived Feynman-Kac formulae for electrode models.

Probabilistic interpretation of the Calderón inverse problem.

Applicable to anisotropic, measurable conductivities.

Abstract

In this paper, we give probabilistic interpretations of both, the forward and the inverse problem of electrical impedance tomography with possibly anisotropic, merely measurable conductivities: Using the theory of symmetric Dirichlet spaces, Feynman-Kac type formulae corresponding to different electrode models on bounded Lipschitz domains are derived. Moreover, we give a probabilistic interpretation of the Calder\'on inverse conductivity problem in terms of reflecting diffusion processes and their corresponding boundary trace processes.