EEG/MEG Source Estimation and Spatial Filtering: The Linear Toolkit

The choice and application of EEG/MEG source estimation methods require an understanding of their underlying modeling assumptions as well as tools to evaluate their spatial resolution and localization performance. Linear methods are the most popular for EEG/MEG source estimation, because most of them are computationally efficient and easy to apply to large data sets. Our chapter will describe essential concepts for the understanding and evaluation of linear methods, also for researchers without a background in signal analysis. These concepts include the superposition principle, resolution matrix, point-spread and cross-talk functions (“leakage”), regularization, and the use of prior information. Due to the superposition principle, linear methods can be meaningfully evaluated on the basis of point sources to draw conclusions about their general resolution properties, i.e., for the case of complex source distributions. On this basis, metrics can be defined to objectively quantify localization accuracy and spatial resolution of linear estimators. We will use those to evaluate the benefit of combining EEG and MEG, as well as to demonstrate the trade-offs made by different source estimation methods between different resolution criteria. We will describe ways to suppress noise via regularization and to incorporate prior knowledge into linear source estimators. The interpretation of linear estimators as spatial filters will be discussed, highlighting special properties of adaptive spatial filters such as beamformers. Finally, we will briefly describe how spatial filters can be flexibly designed using multiple types of constraints.