Random matrix approach for high-frequency fMRI data in a linear model of brain connectivity

Abstract

Current functional brain imaging techniques involve significant stochastic components as seen e.g. in BOLD timeseries of voxels in fMRI measurements. By assuming a linear model of connectedness between voxels in the human brain it is natural to propose a random matrix approach which has been recently successfully applied in financial timeseries. In particular the Marcenco-Pastur law gives a clear criterion to determine those eigenvalues of the correlation matrix which are associated with non-random components in the data matrix - i.e. the signal. The eigenvectors associated with these eigenvalues can be plotted as "eigenimages" which allow a separation of "functional" components of the signal. The approach can be generalized to time-shifted correlation matrices, which could take into account finite propagation times of signals in the brain. The method is demonstrated on a well studied fMRI data set. We discuss similarities and the mathematical overlap to standard PCA approaches to fMRI, and show its usefulness in the context of model-independent detection of timing differences of the BOLD response between regions.