The spatiotemporal MEG covariance matrix modeled as a sum of Kronecker products

The single Kronecker product (KP) model for the spatiotemporal covariance of MEG residuals is extended to a sum of Kronecker products. This sum of KP is estimated such that it approximates the spatiotemporal sample covariance best in matrix norm. Contrary to the single KP, this extension allows for describing multiple, independent phenomena in the ongoing background activity. Whereas the single KP model can be interpreted by assuming that background activity is generated by randomly distributed dipoles with certain spatial and temporal characteristics, the sum model can be physiologically interpreted by assuming a composite of such processes. Taking enough terms into account, the spatiotemporal sample covariance matrix can be described exactly by this extended model. In the estimation of the sum of KP model, it appears that the sum of the first 2 KP describes between 67% and 93%. Moreover, these first two terms describe two physiological processes in the background activity: focal, frequency-specific alpha activity, and more widespread non-frequency-specific activity. Furthermore, temporal nonstationarities due to trial-to-trial variations are not clearly visible in the first two terms, and, hence, play only a minor role in the sample covariance matrix in terms of matrix power. Considering the dipole localization, the single KP model appears to describe around 80% of the noise and seems therefore adequate. The emphasis of further improvement of localization accuracy should be on improving the source model rather than the covariance model.