Ellipsoidal refinement of the regularized inverse: performance in an anatomically realistic EEG model

Functional brain imaging and source localization based on the scalp's potential field requires a solution to the inverse electrostatic problem. This is an underdetermined problem with many solutions. Minimum norm and regularization methods involving the norm are often used, but generally give solutions in which current is widely distributed. One method for reducing the spatial distribution of a solution is to apply it iteratively within the bounds of a shrinking ellipsoid. This paper compares the performance of this approach with an exhaustive search at various noise levels using a numeric simulation of the electroencephalogram in a realistic conductor model. The results show that inverting a single dipolar source with a location accuracy comparable to an exhaustive search requires in the range of 5 to 10 dB higher signal-to-noise ratio.