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

Abstract

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.

Transient oscillation dynamics during sleep provide a robust basis for electroencephalographic phenotyping and biomarker identification

“…This value was chosen to be a highly conservative estimate of the lower bounds of the 1/ f background EEG structure across the night—providing some whitening of the spectrum with minimal disturbance of peak structure. As the non-oscillatory structure is known to change dynamically during sleep [ 58 , 102 ], future iterations of this algorithm may compute the baseline using dynamic state-space modeling methods for 1/ f α and peak estimation [ 76 ]. However, this process is currently computationally intensive and would add significantly to processing time.…”

An iterative search algorithm to identify oscillatory dynamics in neurophysiological time series

“…Iterative Oscillator Search Algorithm necessarily show a peak in the spectrum corresponding to each oscillation [10][11][12]. We take a slightly different approach: we propose that an oscillation is present if the underlying dynamical system that generated the observed signal is oscillatory by nature.…”

“…In previous work, oscillatory structure has been identified by characterizing the shape of the spectrum, with the rationale that an oscillatory signal should necessarily show a peak in the spectrum corresponding to each oscillation [10][11][12]. We take a slightly different approach: we propose that an oscillation is present if the underlying dynamical system that generated the observed signal is oscillatory by nature.…”

“…For instance, as people age, it is well-known that posterior alpha waves can decrease in frequency, sometimes below the canonical 8 to 12 Hz alpha band [5][6][7] and due to individual variation, oscillations such as sleep spindles, which are generally considered to be between 11-16 Hz or conservatively 12-15 Hz, may fall outside the expected frequency range [8,9]. To overcome these problems, recent analysis methods have employed curve-fitting procedures to identify peaks in the power spectrum distinct from broadband noise [10][11][12][13]. The advantage of these approaches is that they are intuitive and are easy to apply using freelyavailable software.…”