Estimating the Number of Sources in Magnetoencephalography Using Spiked Population Eigenvalues

ABSTRACT

Magnetoencephalography (MEG) is an advanced imaging technique used to measure the magnetic fields outside the human head produced by the electrical activity inside the brain. Various source localization methods in MEG require the knowledge of the underlying active sources, which are identified by a priori. Common methods used to estimate the number of sources include principal component analysis or information criterion methods, both of which make use of the eigenvalue distribution of the data, thus avoiding solving the time-consuming inverse problem. Unfortunately, all these methods are very sensitive to the signal-to-noise ratio (SNR), as examining the sample extreme eigenvalues does not necessarily reflect the perturbation of the population ones. To uncover the unknown sources from the very noisy MEG data, we introduce a framework, referred to as the intrinsic dimensionality (ID) of the optimal transformation for the SNR rescaling functional. It is defined as the number of the spiked population eigenvalues of the associated transformed data matrix. It is shown that the ID yields a more reasonable estimate for the number of sources than its sample counterparts, especially when the SNR is small. By means of examples, we illustrate that the new method is able to capture the number of signal sources in MEG that can escape PCA or other information criterion-based methods. Supplementary materials for this article are available online.

KEYWORDS:

• Brain imaging
• Eigenthresholding
• Intrinsic dimensionality
• Inverse MEG problem
• Spiked eigenvalues

Acknowledgments

The authors thank Dr. Anto Bagic for collecting the empty room MEG data and Professor Rob Kass for the BCI data. The authors’ warm thanks also go to three referees and the associate editor for a number of constructive comments.

Additional information

Funding

This research is supported by Yao’s MOE Tier 1 (R-155-000-154-133) and Tier 2 (R-155-000-184-112) Grant Award.