Reconstruction algorithm based on stochastic Galerkin finite element method for electrical impedance tomography

Abstract

Electrical impedance tomography aims at reconstructing the internal conductivity of a physical body from boundary measurements of current and voltage. In this work, the conductivity is modelled as a log-normal random field with a known (prior) distribution, and the reconstruction task is reformulated as a Bayesian inference problem. Combining the prior information with a stochastic Galerkin finite element method, an explicit parametrized approximation is written for the posterior distribution of the conductivity, i.e. for the conditional probability distribution given the boundary measurements, which enables efficient computation of point estimates for the posterior. The feasibility of this approach is demonstrated by two-dimensional numerical examples in the framework of the complete electrode model, which is the most accurate model for practical impedance tomography.