Estimation of Time-Varying Spectral Peaks and Decomposition of EEG Spectrograms

Detection of spectral peaks and estimation of their properties, including frequency and amplitude, are fundamental to many applications of signal processing. Electroencephalography (EEG) of sleep, in particular, displays characteristic oscillations that change continuously throughout the night. Capturing these dynamics is essential to understanding the sleep process and characterizing the heterogeneity observed across individuals. Most sleep EEG analyses rely on either time-averaged spectra or bandpassed amplitude/power. Unfortunately, these approaches obscure the time-variability of peak properties, require specification of a priori criteria, and cannot distinguish power from nearby oscillations. More sophisticated approaches, using various spectral models, have been proposed to better estimate oscillatory properties, but these too have limitations. We present an improved approach to spectrogram decomposition, tracking time-varying parameterized peak functions and dynamically estimating their parameters using a modified form of the iterated extended Kalman filter (IEKF) that incorporates discrete On/Off-switching of peak combinations and a sampling step to draw the initial reference trajectory. We evaluate this approach on two types of simulated examples-one nearly within the model class and one outside. We find excellent performance, in terms of spectral fits and accuracy of estimated states, for both simulation types. We then apply the approach to real EEG data of sleep onset, obtaining quality spectral estimates with estimated peak combinations closely matching the expert-scored sleep stages. This approach offers not only the ability to estimate time-varying parameters of spectral peaks but, moving forward, the potential to estimate the governing dynamics and analyze their variability across nights, subjects, and clinical groups.