Estimation of non-stationary region boundaries in EIT - state estimation approach

We propose a novel numerical approach to the non-stationary electrical impedance tomography (EIT) problem in the case of a piecewise constant conductivity distribution. The assumption is that the body Omega consists of disjoint regions with smooth boundaries and known values of the conductivity. In addition, the region boundaries are assumed to be non-stationary in the sense that they may exhibit significant changes during the acquisition of one traditional EIT frame. In the proposed method, the inverse problem is formulated as a state estimation problem. Within the state estimation formulation the shape representation of the region boundaries is considered as a stochastic process. The objective is to estimate a sequence of states for the time-varying region boundaries, given the temporal evolution model of the boundaries, the observation model and the data on delta Omega. In the proposed method, the state estimates are computed using the extended Kalman filter. The implementation of the method is based on Fourier representation of the region boundaries and on the finite-element method. The performance of the method is evaluated using noisy synthetic data. In addition, the choice of the current injection strategy is discussed and it is found that the use of only a few principal current patterns may lead to substantially better results in nonstationary situations.