State Estimation in Three Dimensional Impedance Imaging

- Use of Fluid Dynamical Evolution Models

A. Seppänen1, M. Vauhkonen1, P.J. Vauhkonen1, E. Somersalo2 and J.P. Kaipio1 1 Department of Applied Physics, University of Kuopio,

P.O.Box 1627, FIN-70211 Kuopio, Finland, Jari.Kaipio@uku.fi 2 Institute of Mathematics, Helsinki University of Technology, P.O.Box 1100 FIN-02015 Helsinki, Finland

ABSTRACT

In this paper we consider the three dimensional impedance imaging of rapidly varying objects. Especially, we concentrate on the case where the target is moving fluid and the time dependence of the object can be described by a stochastic convection-diffusion (CD) model. The observations are made as in ordinary electrical impedance tomography (EIT) but in the reconstruction we take into account the time dependence of the object. The observation model of EIT together with the convection-diffusion model constitute the so-called state-space representation and the reconstruction problem of EIT can be described as the state estimation problem. The state estimation problem is solved with the fixed-lag Kalman smoother algorithm.

Keywords process tomography, electrical impedance tomography, state estimation, Kalman smoother