MODELING THE ELECTROENCEPHALOGRAM BY MEANS OF SPATIAL SPLINE SMOOTHING AND TEMPORAL AUTOREGRESSION

A spatial-temporal model for the description of electroencephalographi c (EEG) data is introduced that combines smooth reconstruction in the spatial domain and autoregressive representation in the time domain. I ts spatial aspect is formulated in a general framework that covers int erpolation, smoothing, and regression. Contrary to the multivariate ti me series models used for EEG analysis up to date, the introduced mode l provides a smooth spatial reconstruction of the EEG cross-spectrum, keeping the condition of nonnegative definiteness. As an instance of p ractical importance, the case in which the spatial reconstruction is b ased on spherical splines is developed in detail. Illustrative example s are presented that show the flexibility of the model to describe bot h normal and abnormal EEG data.