  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.
