A framework for the design of flexible cross-talk functions for spatial filtering of EEG/MEG data: DeFleCT

Brain activation estimated from EEG and MEG data is the basis for a number of time-series analyses. In these applications, it is essential to minimize "leakage" or "cross-talk" of the estimates among brain areas. Here, we present a novel framework that allows the design of flexible cross-talk functions (DeFleCT), combining three types of constraints: (1) full separation of multiple discrete brain sources, (2) minimization of contributions from other (distributed) brain sources, and (3) minimization of the contribution from measurement noise. Our framework allows the design of novel estimators by combining knowledge about discrete sources with constraints on distributed source activity and knowledge about noise covariance. These estimators will be useful in situations where assumptions about sources of interest need to be combined with uncertain information about additional sources that may contaminate the signal (e.g. distributed sources), and for which existing methods may not yield optimal solutions. We also show how existing estimators, such as maximum-likelihood dipole estimation, L2 minimum-norm estimation, and linearly-constrained minimum variance as well as null-beamformers, can be derived as special cases from this general formalism. The performance of the resulting estimators is demonstrated for the estimation of discrete sources and regions-of-interest in simulations of combined EEG/MEG data. Our framework will be useful for EEG/MEG studies applying time-series analysis in source space as well as for the evaluation and comparison of linear estimators.