Probabilistic interpretation of electrical impedance tomography

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 Calderón inverse conductivity problem in terms of reflecting diffusion processes and their corresponding boundary trace processes.

References in corpus (2)

• Time-reversal and elliptic boundary value problems
• A probabilistic approach to Dirichlet problems of semilinear elliptic PDEs with singular coefficients