  Electrical impedance tomography (EIT) is an imaging modality in which the
conductivity distribution inside a target is reconstructed based on voltage
measurements from the surface of the target. Reconstructing the conductivity
distribution is known to be an ill-posed inverse problem, the solutions of
which are highly intolerant to modelling errors. In order to achieve sufficient
accuracy, very dense meshes are usually needed in a finite element
approximation of the EIT forward model. This leads to very high-dimensional
problems and often unacceptably tedious computations for real-time
applications. In this paper, the model reduction in EIT is considered within
the Bayesian inversion framework. We construct the reduced-order model by
proper orthogonal decompositions (POD) of the electrical conductivity and the
potential distributions. The associated POD modes are computed based on a
priori information on the conductivity. The feasibility of the reduced-order
model is tested both numerically and with experimental data. In the selected
test cases, the proposed model reduction approach speeds up the computation by
more than two orders of magnitude in comparison with the conventional EIT
reconstruction, without decreasing the quality of the reconstructed images
significantly.
