A space-frequency analysis of MEG background processes

In MEG source localization the estimated source parameters will be more reliable when the spatiotemporal covariance of the noise and background activity is taken into account. Since this covariance is in general too large to estimate based on the data and to invert efficiently, different parametrizations have been proposed in the literature. These models can be seen as special cases of the general decomposition of the covariance into a sum of Kronecker products of spatial matrices X(n) and temporal matrices T(n) (Van Loan, 2000). In this study we investigate the assumption of the matrices T(n) being Toeplitz. If so, the covariance matrix in the space-frequency domain will have an approximate block-diagonal structure, facilitating inversion, which is a prerequisite for source localization. In this study we address the question whether the Toeplitz approximation is valid for data sets obtained in visual evoked field, auditory evoked field, somatosensory evoked field experiments and data sets containing spontaneous activity. It turns out that on average 87% is in the block-diagonal of the sample covariance, which is close to the values obtained for real Toeplitz matrices T(n). This implies that the space-frequency domain is very interesting for source localization since the major part of the entire covariance can be incorporated in that domain straightforwardly. Finally, the two major processes in the background activity are characterized in terms of their spatial and frequency patterns, yielding a focal and a non-focal pattern in 8 of 10 data sets analyzed in this study. The focal pattern represents the alpha frequency at parieto-occipital areas, whereas the non-focal pattern is more widespread both in space and in frequency.