The Bayesian Formulation of EIT: Analysis and Algorithms

TL;DR

This paper develops a rigorous Bayesian framework for Electrical Impedance Tomography (EIT), analyzing different prior models and demonstrating their effectiveness through numerical simulations in reconstructing binary fields.

Contribution

It introduces a formal Bayesian formulation of EIT in infinite dimensions and compares three prior models for binary field reconstruction.

Findings

Bayesian formulation ensures well-posedness in the Hellinger metric.

Star-shaped prior performs best in binary field reconstruction.

Posterior distributions exhibit distinct properties depending on the prior used.

Abstract

We provide a rigorous Bayesian formulation of the EIT problem in an infinite dimensional setting, leading to well-posedness in the Hellinger metric with respect to the data. We focus particularly on the reconstruction of binary fields where the interface between different media is the primary unknown. We consider three different prior models - log-Gaussian, star-shaped and level set. Numerical simulations based on the implementation of MCMC are performed, illustrating the advantages and disadvantages of each type of prior in the reconstruction, in the case where the true conductivity is a binary field, and exhibiting the properties of the resulting posterior distribution.