Stochastic Galerkin Finite Element Method with Local Conductivity Basis for Electrical Impedance Tomography

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 by 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.