Spatial filter approach for evaluation of the surface Laplacian of the electroencephalogram and magnetoencephalogram

The surface Laplacian is a technique that has been utilized to improve the spatial resolution of the electroencephalogram (EEG) and the magnetoencephalogram (MEG). We investigate the amount of improvement to the spatial resolution afforded by the surface Laplacian by examining the spatial filters that describe the relationship between cortical current sources and the surface Laplacian. The surface Laplacian spatial filters extend into higher spatial frequencies than do raw signal spatial filters, particularly for EEG Laplacian spatial filters, indicating that substantial improvement in spatial resolution is possible. However, the response of the surface Laplacian operation to the nature and amount of noise in the raw EEG and MEG signals is of paramount importance. Spatially correlated noise, coupled with uncorrelated noise, requires additional regularization of inverse spatial filters resulting in a decrease in spatial resolution. Substantial improvements in spatial resolution may be obtained using the surface Laplacian techniques as long as correlated noise levels are small and raw signals have relatively high signal-to-noise ratios.