Posterior covariance related optimal current patterns in electrical impedance tomography

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 difference of voltage measurements 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 this paper, 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. Also, it is shown that in some cases only a few current patterns are needed in order to exhaust most of the information available in EIT measurements in the sense that conducting further measurements does not considerably decrease the uncertainty related to the estimates.