EEG dipole localization bounds and MAP algorithms for head models with parameter uncertainties

Abstract
The Cramer-Rao bound for unbiased dipole location estimation is derived under the assumption of a general head model parameterized by deterministic and stochastic parameters. The expression thus characterizes fundamental limits on EEG dipole localization performance due to the effects of both model uncertainty and statistical measurements noise. Expressions are derived for the cases of multivariate Gaussian and gamma distribution priors, and examples are given to illustrate the derived bounds when the radii and conductivities of a four-concentric sphere head model are allowed to be random. The joint MAP estimate of location/model parameters is then examined as a means of achieving robustness to deviations from an ideal head model. Random variations in both the multiple sphere radii and the layer conductivities are shown, via the stochastic Cramer-Rao bounds and Monte Carlo simulation of the MAP estimator, to have the most impact on localization performance in high SNR regions, where finite sample effects are not the limiting factors. This corresponds most often to spatial regions that are close to the scalp electrodes.

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