A reduced-order filtering approach for 3D dynamical electrical impedance tomography

Recently, it has been shown that the state estimation approach to process tomography can provide estimates that are significantly better than (a sequence of) conventional stationary snapshot estimates. One of the main obstacles of the adoption of the recursive state estimation algorithms, most commonly different versions of the Kalman filter, is the computational complexity. This is due to both the required large dimension for the state variable and the need to use iterative versions of the Kalman filter in such cases in which there are large contrasts or varying background. In this paper, we propose to use a reduced-order representation for the state variable. In particular, we propose to use the proper orthogonal decomposition-related basis for the state. We consider a simulation study with fluctuating background conductivity, and, in particular, with fluctuating contact impedances. We compare the proposed approach to three different versions of the Kalman filter having different computational complexities. We show that this approach allows the reduction of the dimension of the problem approximately by an order of magnitude and yields essentially as accurate estimates as the most accurate traditional Kalman filter version, the iterated extended Kalman filter.