Source reconstruction of broadband EEG/MEG data using the frequency-adaptive broadband (FAB) beamformer

Abstract

A beamformer enhances the signal from a voxel of interest by minimising interference from all other locations represented in the sensor covariance matrix. However, the presence of narrowband oscillations in EEG/MEG implies that the spatial structure of the covariance matrix, and hence also the optimal beamformer, depends on the frequency. The frequency-adaptive broadband (FAB) beamformer introduced here exploits this fact in the Fourier domain by partitioning the covariance matrix into cross-spectra corresponding to different frequencies. For each frequency bin, an individual spatial filter is constructed. This assures optimal noise suppression across the frequency spectrum. After applying the spatial filters in the frequency domain, the broadband source signal is recovered using the inverse Fourier transform. MEG simulations using artificial data and real resting-state measurements were used to compare the FAB beamformer to the LCMV beamformer and MNE. The FAB beamformer significantly outperforms both methods in terms of the quality of the reconstructed time series. To our knowledge, the FAB beamformer is the first beamforming approach tailored for the analysis of broadband neuroimaging data. Due to its frequency-adaptive noise suppression, the reconstructed source time series is suited for further time-frequency or connectivity analysis in source space. Introduction 1 Electroencephalography (EEG) and magnetoencephalography (MEG), jointly 2 abbreviated as MEEG here, measure the electrical currents or magnetic fields associated 3 with synchronised activity of neuronal populations [1-3]. Compared to hemodynamic 4 methods such as functional magnetic resonance imaging (fMRI), the Achilles' heel of 5 MEEG is the low accuracy in localising the sources. Since the sensors are located at a 6 distance to the brain, the activity of brain sources needs to be statistically 7 reconstructed. The inverse problem of estimating the sources from the sensor 8 measurements is underconstrained because the number of sources exceeds the number of 9 sensors. Furthermore, neurons in some subcortical areas are aligned such that they 10 constitute a closed field, producing little measurable electrical activity [1]. Consequently, 11 in order to obtain a unique solution, additional assumptions about the sources (such as 12 their uncorrelatedness) are required to constrain the inverse model [4, 5]. The linear 13 forward model of MEEG, specifying how activity in the brain projects into the sensors, 14 can be formulated as 15 December 17, 2018 1/15 42 The principal assumption for beamforming is that all sources are uncorrelated and 43 hence the source covariance matrix C s is diagonal. Indeed, inserting a diagonal source 44 covariance matrix into Eq 2 leads to a scaled version of the beamformer solution in Eq 3. 45 Recently, it has been shown that LCMV beamforming is formally equivalent to Linear 46 Discriminant Analysis (LDA) [16]. 47 318 Fourier domain representation of a Morlet wavelet. The time-frequency trade-off was 319determined by setti...