Multi-scale wavelet coherence with applications to brain connectivity

Music City Center 

The goal in this paper is to develop a novel statistical approach to characterize functional interactions between channels in a brain network. Wavelets are effective for capturing transient properties of nonstationary signals because they have compact support that can be compressed or stretched according to the dynamic properties of the signal. Wavelets give a multi-scale decomposition of signals and thus can be used for studying potential cross-scale interactions between signals. To achieve this, we develop the scale-specific subprocesses of a multivariate locally stationary wavelet stochastic process. Under this proposed framework, a novel cross-scale dependence measure is developed. This provides a measure for the dependence structure of components at different scales of multivariate time series. Extensive simulation studies are conducted to demonstrate that the theoretical properties hold in practice. The proposed cross-scale analysis is applied to the electroencephalogram (EEG) data to study alterations in the functional connectivity structure in children diagnosed with attention deficit hyperactivity disorder (ADHD). Our approach identified novel interesting cross-scale interactions between channels in the brain network.

Local stationarity

Multi-resolution analysis

Non-stationary time series

Scale-specific processes

Wavelets process