MEG beamforming using Bayesian PCA for adaptive data covariance matrix regularization

Abstract

Beamformers are a commonly used method for doing source localisation from magnetoencephalography (MEG) data. A key ingredient in a beamformer is the estimation of the data covariance matrix. When the noise levels are high, or when there is only a small amount of data available, the data covariance matrix is estimated poorly and the signal-to-noise ratio (SNR) of the beam-former output degrades. One solution to this is to use regularization whereby the diagonal of the covariance matrix is amplified by a pre-specified amount. However, this provides improvements at the expense of a loss in spatial resolution, and the parameter controlling the amount of regularization must be chosen subjectively. In this paper, we introduce a method that provides an adaptive solution to this problem by using a Bayesian Principle Component Analysis (PCA). This provides an estimate of the data covariance matrix to give a data-driven, non-arbitrary solution to the trade-off between the spatial resolution and the SNR of the beamformer output. This also provides a method for determining when the quality of the data covariance estimate maybe under question. We apply the approach to simulated and real MEG data, and demonstrate the way in which it can automatically adapt the regularization to give good performance over a range of noise and signal levels.

Altered cortical beta‐band oscillations reflect motor system degeneration in amyotrophic lateral sclerosis

“…Estimates of the data covariance matrix were regularized by removing the weakest PCA components [Woolrich et al, 2011] to leave only 61 (the approximate rank of the data after the use of Maxfilter and removal of two ICA components pertaining to (a) ECG and (b) eye‐movement artefacts). Cue, response and movement termination locked epochs were then inspected across 8‐mm whole‐brain grids to locate subject specific, functionally defined regions of interest (ROIs) corresponding to cortical motor regions: for each subject, the MNI coordinates separately pertaining to either the maximal preparatory ERD, response ERD or PMBR were selected for each hemisphere (locations depicted in Supporting Information Figure S1).…”

Frontoparietal and Cingulo-opercular Networks Play Dissociable Roles in Control of Working Memory

“…To characterize the time course of activation in each ROI, a virtual electrode was created for each ROI coordinate using a linearly constrained minimum variance beamformer ( Woolrich, Hunt, Groves, & Barnes, 2011). The time-frequency representation of the data was then computed at each virtual electrode, between 3 and 30 Hz.…”

Magnetoencephalography

“…1 ▸ Two distinct cerebral regions can facilitate preferential information exchange by synchronising their rhythmic behaviour; the γ band (40-80 Hz), in particular, facilitates this process, but is also modulated 'top-down' by lower frequencies such as θ (4-7 Hz), reflecting factors, such as arousal states. ▸ α Rhythms (8)(9)(10)(11)(12)(13), so prominent in the occipital cortex upon eye closure, reflect more than just an 'idling' rhythm but also contribute to active allocation of attentional resources and suppress irrelevant sensory information. 2 ▸ The influential theory 'Communication through Coherence' developed by Fries, 3 builds on existing models of 'binding by synchronisation' that may underpin selective attention, a key function in prioritising neural events to guide awareness and action.…”

“…This method, originally developed for use in radar arrays, corresponds to an adaptive spatial filter designed to extract the origins of a signal from some prespecified spatial location. 10 MEG data in either 'sensor space' ( presented as data recorded across the distribution of the sensors) or 'source space' (reconstructed to a 3D model of brain sources) offer a wealth of analysis possibilities and selected features that can relate to a particular clinical question (figure 5).…”