Estimation of non-stationary region boundaries in EIT—state estimationapproach

Abstract

We propose a novel numerical approach to the non-stationary electricalimpedance tomography (EIT) problem in the case of a piecewise constantconductivity distribution. The assumption is that the body Ωconsists of disjoint regions with smooth boundaries and known values ofthe conductivity. In addition, the region boundaries are assumed to benon-stationary in the sense that they may exhibit significant changes during theacquisition of one traditional EIT frame. In the proposed method, the inverseproblem is formulated as a state estimation problem. Within the stateestimation formulation the shape representation of the region boundaries isconsidered as a stochastic process. The objective is to estimate a sequence ofstates for the time-varying region boundaries, given the temporal evolutionmodel of the boundaries, the observation model and the data on ∂Ω. In the proposed method, the state estimates are computedusing the extended Kalman filter. The implementation of the methodis based on Fourier representation of the region boundaries and on thefinite-element method. The performance of the method is evaluated using noisysynthetic data. In addition, the choice of the current injection strategy isdiscussed and it is found that the use of only a few principal currentpatterns may lead to substantially better results in non-stationary situations.