A method for reducing cross-talk in MEG data with subspace suppression and the nulling beamformer

Introduction

Source localization in Magnetoencephalography (MEG) is a difficult ill-posed problem where the appropriate method depends on the nature of the analysis. Studies often involve analysis of a sparse set of Regions of Interest (ROIs) over the cortex, such as in (Vaina 2010). A simple solution involves computing the minimum norm estimate (MNE)(Hämäläinen 1994) and averaging over all vertex sources in each ROI. Due to the large point spread function, the regions should be far apart to avoid cross talk. The nulling beamformer overcomes the cross talk problem by “nulling” the gain produced by interfering source locations (Hui 2010).  Each ROI’s lead field matrix needs to be reduced in rank in order to prevent overconstraining the problem.  Hui et al. perform a truncated Singular Value Decomposition (TSVD), but this will not necessarily produce matrices with minimal subspace angles, especially if two ROIs are close neighbors.  We propose a new method, Subspace Suppression (SS), where the number of singular values along with a tuning parameter allow for controlling crosstalk through suppressing singular vectors that project into the lead field matrices of interfering ROIs.

Approach

Subspace Suppression: For each ROI, we form a gain matrix that maps the activity at each vertex within the ROI to the sensors.  In (Hui 2010), the TSVD is applied to lower the rank of these matrices to avoid overconstraining the problem.  However, if an ROI and its neighboring ROIs have similar mappings from the source space to the sensor space over the largest singular vectors, then the method would fail to appropriately nullify the contribution from the neighbors.  Instead, the Subspace Suppression method removes, from the total gain of the original gain matrix, the projections that have high gain in neighboring ROIs, with alpha as a tuning parameter controlling the amount of removal.  The TSVD is applied to the resulting gain matrix.  Note that vectors that strongly overlapped with neighbors are suppressed and thus will have lower corresponding singular values, and will be less likely to be included in the truncation.  Also, note that setting alpha to zero, that is, there is no removal of the projections, will not apply Subspace Suppression, thus reducing the method to the same as in (Hui 2010).

Parameter Selection: We choose the optimal alpha and the optimal truncation point for the TSVD.  However, the concept of an optimal parameter is ill-defined. Our approach is to optimize parameters over the cross-talk SNR (ctSNR), which we define as the ratio of the signal amplitude in an active area over the cross-talk amplitude.  Through simulation, we find parameters that maximize the ctSNR.

Data Simulation: The synthetic data was generated on the subject’s brain from the dataset from (Vaina 2010) using the mne_simu function of the MNE software.  A 200 ms square pulse starting at 0 ms is generatedi n the Aud ROI in the right hemisphere followed by another 200 ms square pulse generated in the STS label starting at 300 ms.  This stimulus is repeated 300 times over 700 ms periods and averaged.  

Results  

Hui, H.B. (2010), 'Identifying true cortical interactions in MEG using the nulling beamformer', NeuroImage, Vol. 49, No. 4. (15 February 2010), pp. 3161-3174. 

Vaina L.M. (2010), 'Long-range coupling of prefrontal cortex and visual (MT) or polysensory (STP) cortical areas in motion perception', BIOMAG2010, IFBME Proceedings Series, Springer Verlag IFBME.