Conditionally Gaussian Hypermodels for Cerebral Source Localization

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Abstract
Bayesian modeling and analysis of the magnetoencephalography and electroencephalography modalities provide a flexible framework for introducing prior information complementary to the measured data. This prior information is often qualitative in nature, making the translation of the available information into a computational model a challenging task. We propose a generalized gamma family of hyperpriors which allows the impressed currents to be focal and we advocate a fast and efficient iterative algorithm, the iterative alternating sequential algorithm for computing maximum a posteriori (MAP) estimates. Furthermore, we show that for particular choices of the scalar parameters specifying the hyperprior, the algorithm effectively approximates popular regularization strategies such as the minimum current estimate and the minimum support estimate. The connection between priorconditioning and adaptive regularization methods is also pointed out. The posterior densities are explored by means of a Markov chain Monte Carlo strategy suitable for this family of hypermodels. The computed experiments suggest that the known preference of regularization methods for superficial sources over deep sources is a property of the MAP estimators only, and that estimation of the posterior mean in the hierarchical model is better adapted for localizing deep sources.