Stochastic Galerkin finite element method with local conductivity basis for electrical impedance tomography

TL;DR

This paper develops a stochastic Galerkin finite element method with local conductivity basis to improve electrical impedance tomography by efficiently propagating uncertainty and reconstructing conductivity from boundary measurements.

Contribution

It introduces a novel stochastic Galerkin approach for modeling conductivity as a random field and reconstructs it using Bayesian methods with experimental validation.

Findings

Accurate uncertainty propagation in conductivity estimation

Effective reconstruction of conductivity and contact resistances

Validated approach with real water tank data

Abstract

The objective of electrical impedance tomography is to deduce information about the conductivity inside a physical body from electrode measurements of current and voltage at the object boundary. In this work, the unknown conductivity is modeled as a random field parametrized by its values at a set of pixels. The uncertainty in the pixel values is propagated to the electrode measurements by numerically solving the forward problem of impedance tomography by a stochastic Galerkin finite element method in the framework of the complete electrode model. For a given set of electrode measurements, the stochastic forward solution is employed in approximately parametrizing the posterior probability density of the conductivity and contact resistances. Subsequently, the conductivity is reconstructed by computing the maximum a posteriori and conditional mean estimates as well as the posterior covariance. The functionality of this approach is demonstrated with experimental water tank data.