Non-local Boundary Conditions and Domain Truncation in Electrical Impedance Tomography

Abstract:  In electrical impedance tomography (EIT), the goal is to estimate an unknown electric conductivity distribution inside a body from current/voltage measurements at the boundary of the body. A common problem arising in numerous applications is that the data can be collected only on a part of the boundary, or the body is infinite and a truncation of the computational domain is needed. Computationally, the domain can be decomposed in two subdomains with a non-local Steklov-Poincare' boundary condition along the cut; however, in the EIT, this boundary condition depends on the unknown conductivity, and therefore constitutes part of the inverse problem. In this talk, we address this problem in a computational Bayesian framework, modeling the boundary condition as part of the unknown to be estimated, and propose a sampling-based method to marginalize the model with respect to the unknown boundary condition.