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 accuracy of the conductivity estimates can be described by the posterior covariance. We propose to optimize the current patterns based on
criteria that are functionals of the posterior covariance matrix. This approach uses the linearized likelihood distribution and results in
nonlinear optimization problems with nonlinear equality constraints. We show that optimal current patterns can be constructed for such
cases in which the distinguishability approach cannot be employed.
We shall also consider the nonstationary inversion case which is especially relevant in the imaging of fast moving fluids. In this case the posterior covariance obeys the so-called Riccati equation. Previous results in simpler settings have suggested that when the optimal state estimation approach is used in the nonstationary case, it may be advisable to use only a single or a few repeated current patterns.
We discuss both purely computational results as well as a real measurement case.
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