Reduced-order model for electrical impedance tomography based on proper   orthogonal decomposition
  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. 
Antti Lipponen, Aku Sepp\"anen and Jari Kaipio
math-ph math.MP