Subspace based Multiple Constrained Minimum Variance (SMCMV) Beamformers

Abstract In Magnetoencephalography (MEG) and Electroencephalography (EEG) two popular approaches are often used for spatial localization of focal task- or stimuli-related brain activations. One is Multiple Signal Classification (MUSIC) approach in the form of Recursively Applied and Projected (RAP) or Truncated RAP (TRAP) MUSIC algorithms. Another one is Multiple Constrained Minimum Variance (MCMV) beamformer method capable of dealing with multiple correlated activations. Considering simplicity, accuracy and computational efficiency both have their advantages and disadvantages. Using these two techniques as a starting point, three main developments were made in this study. First, we introduced novel Subspace based MCMV (or SMCMV) beamformers whose localizer functions combine MUSIC and MCMV localizers. Second, we showed analytically that SMCMV localizers in principle allow precise identification of n arbitrarily correlated sources irrespective to their strength in exactly n scans of the brain volume. Third, using extensive simulations and ANOVA statistical analyses we showed that on average SMCMV outperforms both the TRAP MUSIC and MCMV Multi-step Iterative Approach (MIA) procedure, currently the most accurate MCMV algorithm to our knowledge, with respect to localization accuracy and the number of successfully identified sources. Importantly, this was demonstrated for situations when the noise covariance could not be estimated precisely, signal to noise ratios were small, source correlations were significant and larger numbers of sources were involved. SMCMV advantage held for both MEG and EEG modalities. In addition we illustrated the SMCMV method by applying it to a real MEG Auditory Steady State Response (ASSR) experiment.