  In this paper we introduce a covariance framework for the analysis of EEG and
MEG data that takes into account observed temporal stationarity on small time
scales and trial-to-trial variations. We formulate a model for the covariance
matrix, which is a Kronecker product of three components that correspond to
space, time and epochs/trials, and consider maximum likelihood estimation of
the unknown parameter values. An iterative algorithm that finds approximations
of the maximum likelihood estimates is proposed. We perform a simulation study
to assess the performance of the estimator and investigate the influence of
different assumptions about the covariance factors on the estimated covariance
matrix and on its components. Apart from that, we illustrate our method on real
EEG and MEG data sets.
  The proposed covariance model is applicable in a variety of cases where
spontaneous EEG or MEG acts as source of noise and realistic noise covariance
estimates are needed for accurate dipole localization, such as in evoked
activity studies, or where the properties of spontaneous EEG or MEG are
themselves the topic of interest, such as in combined EEG/fMRI experiments in
which the correlation between EEG and fMRI signals is investigated.
