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The phase-reset model of oscillatory EEG activity has received a lot of attention in the last decades for decoding different cognitive processes. Based on this model, the ERPs are assumed to be generated as a result of phase reorganization in ongoing EEG. In addition, the study of oscillatory EEG signals can be used to overcome limitations regarding the study of segmented EEG data, i.e., ERPs. Measuring the level of instantaneous phase (IP) synchronization has been used in numerous studies of ERPs as well as oscillatory activity for a better understanding of the underlying neural activities. However, the reliability of results can be challenged as a result of noise artefact in IP. Phase distortion due to environmental noise artifacts as well as different pre-processing steps on signals can lead to generation of artificial phase jumps. One of such effects presented recently is the effect of low envelope on the IP of signal. It has been shown that as the instantaneous envelope of the analytic signal approaches zero, the variations in the phase increase, effectively leading to abrupt transitions in the phase. These abrupt transitions can distort the phase synchronization results as they are not related to any neurophysiological effect. These transitions are called spurious phase variation. In this study, we present a model to remove generated artificial phase variations due to the effect of low envelope. The proposed method is based on a simplified form of a Kalman smoother, that is able to model the IP behavior in narrow-bandpassed oscillatory signals. The method is not only evaluated on synthetic data but also in experimental EEG measurements recorded using a listening dichotic paradigm designed to assess auditory selective attention between an attended and unattended conditions.
We study the effect of long-term habituation signatures of auditory selective attention reflected in the instantaneous phase information of the auditory event-related potentials (ERPs) at four distinct stimuli levels of 60, 70, 80, and 90 dB SPL. The analysis is based on the single-trial level. The effect of habituation can be observed in terms of the changes (jitter) in the instantaneous phase information of ERPs. In particular, the absence of habituation is correlated with a consistently high phase synchronization over ERP trials. We estimate the changes in phase concentration over trials using a Bayesian approach, in which the phase is modeled as being drawn from a von Mises distribution with a concentration parameter which varies smoothly over trials. The smoothness assumption reflects the fact that habituation is a gradual process. We differentiate between different stimuli based on the relative changes and absolute values of the estimated concentration parameter using the proposed Bayesian model.
