Abstract
Beamforming is a popular method for functional source reconstruction using magnetoencephalography (MEG) and electroencephalography (EEG) data. Beamformers, which were first proposed for MEG more than two decades ago, have since been applied in hundreds of studies, demonstrating that they are a versatile and robust tool for neuroscience. However, certain characteristics of beamformers remain somewhat elusive and there currently does not exist a unified documentation of the mathematical underpinnings and computational subtleties of beamformers as implemented in the most widely used academic open source software packages for MEG analysis (Brainstorm, FieldTrip, MNE, and SPM). Here, we provide such documentation that aims at providing the mathematical background of beamforming and unifying the terminology. Beamformer implementations are compared across toolboxes and pitfalls of beamforming analyses are discussed. Specifically, we provide details on handling rank deficient covariance matrices, prewhitening, the rank reduction of forward fields, and on the combination of heterogeneous sensor types, such as magnetometers and gradiometers. The overall aim of this paper is to contribute to contemporary efforts towards higher levels of computational transparency in functional neuroimaging.
Highlights
Created for sonar and radar applications, the beamforming technique has been introduced into neuroscience as a method for interpreting the neural basis of MEG and EEG data (van Drongelen et al, 1996; Van Veen and Buckley, 1988; Van Veen et al, 1997)
While detailed resources on the mathematical foundations of beamformers for neuroscience exist (e.g., Hillebrand and Barnes, 2005; Sekihara and Nagarajan, 2008; 2015), it is not always straightforward to link these to the beamformer implementations available in M/EEG toolboxes that are frequently used in practice
In this technical note we provided a concise overview of the beamformers that are most commonly used for source reconstruction of EEG and MEG data
Summary
Created for sonar and radar applications, the beamforming technique has been introduced into neuroscience as a method for interpreting the neural basis of MEG and EEG data (van Drongelen et al, 1996; Van Veen and Buckley, 1988; Van Veen et al, 1997). Since its first implementation in neuroscientific open source toolboxes (namely, Nutmeg [Dalal et al, 2004; Dalal et al, 2011] and FieldTrip [Oostenveld et al, 2011]), beamforming has become a widely applied source reconstruction technique in the field and is implemented in various M/EEG signal processing software packages Features such as the ability to resolve deeper sources (Backus et al, 2016; Quraan et al, 2011; Wilson et al, 2010) or to suppress external noise (Litvak et al, 2010; Sekihara et al, 2004) make them widely used for the source analysis of M/EEG data. In practical applications, recording device dependent data properties require specific processing of the data to optimize the analysis
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