A mathematical approach to the temporal stationarity of background noise in MEG/EEG measurements.

The general spatiotemporal covariance matrix of the background noise in MEG/EEG signals is huge. To reduce the dimensionality of this matrix it is modeled as a Kronecker product of a spatial and a temporal covariance matrix. When the number of time samples is larger than, say, J = 500, the iterative Maximum Likelihood estimation of these two matrices is still too time-consuming to be useful on a routine basis. In this study we looked for methods to circumvent this computationally expensive procedure by using a parametric model with subject-dependent parameters. Such a model would additionally help with interpreting MEG/EEG signals. For the spatial covariance, models have been derived already and it has been shown that measured MEG/EEG signals can be understood spatially as random processes, generated by random dipoles. The temporal covariance, however, has not been modeled yet, therefore we studied the temporal covariance matrix in several subjects. For all subjects the temporal covariance shows an alpha oscillation and vanishes for large time lag. This gives rise to a temporal noise model consisting of two components: alpha activity and additional random noise. The alpha activity is modeled as randomly occurring waves with random phase and the covariance of the additional noise decreases exponentially with lag. This model requires only six parameters instead of 12 J(J + 1). Theoretically, this model is stationary but in practice the stationarity of the matrix is highly influenced by the baseline correction. It appears that very good agreement between the data and the parametric model can be obtained when the baseline correction window is taken into account properly. This finding implies that the background noise is in principle a stationary process and that nonstationarities are mainly caused by the nature of the preprocessing method. When analyzing events at a fixed sample after the stimulus (e.g., the SEF N20 response) one can take advantage of this nonstationarity by optimizing the baseline window to obtain a low noise variance at this particular sample.