Statistics and Its Interface

Volume 15 (2022)

Number 3

Depth-invariant beamforming for functional connectivity with MEG data

Pages: 359 – 371



Jian Zhang (School of Mathematics, Statistics and Actuarial Science, University of Kent, Canterbury, Kent, United Kingdom)


The conventional beamformers that reconstruct the cerebral origin of brain activity measured outside the head via electro- and magneto-encephalography (EEG/MEG) suffer from depth bias and smearing of nearby sources. Here, to meet these methodological challenges, we propose a depth-invariant and forward beamformer for magneto-encephalography (MEG) data. Based on the new proposal, we further develop a two-step approach for inferring functional connectivity in the brain. The proposed methodology is invariant with respect to source depths in the brain. It nulls smearing of nearby sources and allows for time-varying source orientations. We illustrate the new approach with MEG data derived from a face-perception experiment, revealing patterns of functional connectivity for face perception. We identify a set of brain regions where their responses and connectivity are significantly varying when stimuli alter between faces and scrambled faces. By simulation studies, we show that the proposed forward beamformer can outperform the forward methods based on conventional beamformers in terms of localization bias.


MEG neuroimaging, depth-invariant beamforming, functional network, source localization, reconstruction

2010 Mathematics Subject Classification


Received 17 August 2020

Accepted 18 August 2021

Published 14 February 2022