Recursive estimation of fast impedance changes in electrical impedance tomography and a related problem

We propose a method for the estimation of fast impedance changes in electrical, impedance tomography (EIT) and wire tomography (WT). WT is a novel method for the estimation of the temperature profiles of gas flows: a matrix of metal wires whose impedance depends on the temperature (such as nickel or platinum) are placed in the how and the resistances of each individual wire are tracked. In the EIT problem the impedance changes are assumed to be so fast that all observations an which the reconstruction is based, can not be assumed to be (even approximately) from the same impedance distribution. The proposed method is based on the formulation of the EIT and WT problems first as dynamical state estimation problems and then solving the mean square estimates for the state (discretized impedance distribution) recursively with the Kalman filter. The appropriate evolution models for EIT include generally random walk-based models and in some applications, e.g. human, thorax, compartmental models. The evolution model of WT comes directly from the associated parabolic partial differential equation (heat equation).