Matching Pursuit Based Dynamic Phase-Amplitude Coupling Measure

Abstract

Long-distance neuronal communication in the brain is enabled by the interactions across various oscillatory frequencies. One interaction that is gaining importance during cognitive brain functions is phase amplitude coupling (PAC), where the phase of a slow oscillation modulates the amplitude of a fast oscillation. Current techniques for calculating PAC provide a numerical index that represents an average value across a pre-determined time window. However, there is growing empirical evidence that PAC is dynamic, varying across time. Current approaches to quantify time-varying PAC relies on computing PAC over sliding short time windows. This approach suffers from the arbitrary selection of the window length and does not adapt to the signal dynamics. In this paper, we introduce a data-driven approach to quantify dynamic PAC. The proposed approach relies on decomposing the signal using matching pursuit (MP) to extract time and frequency localized atoms that best describe the given signal. These atoms are then used to compute PAC across time and frequency. As the atoms are time and frequency localized, we only compute PAC across time and frequency regions determined by the selected atoms rather than the whole time-frequency range. The proposed approach is evaluated on both simulated and real electroencephalogram (EEG) signals.