Studies of parameter estimation and uncertainty in array processing with applications in EEG dipole localization

Multiple current dipole localization from electroencephalogram (EEG) data is currently an active field of research because it has the potential to provide an objective measure of functional brain activity at millisecond resolution and relatively low cost. Much insight can be gained with regard to dipole localization when cast as a special case of the more general source localization problem in array processing. In both instances, the primary parameters of interest are associated with location in space, and they enter into physical propagation/observation models nonlinearly.; In addition to the unknown source locations, all practical localization algorithms depend either implicitly or explicitly on a number of secondary (nuisance) parameters. In this thesis we utilize a Bayesian statistical framework to represent various degrees of uncertainty in secondary parameters. One such set in EEG dipole localization is associated with the head model. By employing a probabilistic model for a general collection of head parameters we derive a stochastic Cramer-Rao bound on dipole localization error in the presence of perturbations from an ideal model. This basic approach also provides a maximum a posteriori (MAP) procedure for robust dipole localization.; Another class of nuisance parameters given a Bayesian treatment in this thesis is that associated with the source signals. For EEG this corresponds to the time-varying amplitude and orientation of each dipole. By assuming a normalizable, yet reasonably broad, prior density function these parameters are integrated out of the full likelihood function. The result is a novel Bayesian marginal for source localization that outperforms the standard conditional maximum likelihood technique for combinations of low signal to noise ratio and/or a small number of sensors. This marginal is also used to derive a new model selection criterion, based on the Bayesian evidence of each proposed model.; Finally, the theme of uncertainty within model selection is extended by deriving the variance of MUSIC location estimates under the assumption that the number of sources has been under-estimated.