Statistical Inversion Approach for Optimizing Current Patterns in EIT

Jari P Kaipio1, Aku Seppänen1, Erkki Somersalo2 and Heikki Haario3

1Department of Applied Physics, University of Kuopio, P.O. Box 1627, FIN-70211 Kuopio, Finland Jari.Kaipio@uku.fi

2Institute of Mathematics, Helsinki University of Technology, P.O. Box 1100 FIN-02015 TKK, Finland esomersa@dopey.hut.fi

3Department of Mathematics, University of Helsinki, P.O. Box 4, FIN-00014, Finland

heikki.haario@helsinki.fi

ABSTRACT

Within the deterministic inversion framework the optimal current pattern theory of electrical impedance tomography is well developed. This theory focuses on the notion of distinguishability, which amounts to optimizing the current patterns so that the voltage measurement difference corresponding to two different predetermined conductivity distributions is maximized. However, it is often difficult to specify the two conductivity distributions. Especially in the framework of statistical inversion theory in which prior information is specified in the form of probability distributions, other approaches are needed. In the statistical inversion framework the mean accuracy of the conductivity estimates can be described by the posterior covariance. In manuscript (Kaipio, 2003) we have proposed to optimize the current patterns based on criteria that are functionals of the posterior covariance matrix.

In this paper we consider the concept of optimal current patterns in the non-stationary inversion case, which is especially relevant in imaging of fast moving fluids. In this case the posterior covariance obeys the so-called Riccati equation. Our previous results in simpler settings have suggested that when the optimal state estimation approach is used in the non-stationary case, it may be advisable to use only a few repeated current patterns. In this paper we study the problem in the case of flow fields.