Removal of spurious phase variations in oscillatory signals

The study of oscillatory electroencephalogram (EEG) data has been one of the main sources for the analysis of different brain functions and decoding a variety of cognitive processes. One of the interesting features that has been the focus of study in the last decades is the study of instantaneous phase information in EEG. Phase synchronization techniques are among the main analysis tools that measure the degree of phase re-organization in signals. In phase re-organization approach, the phase alignment in stimulus induced potentials has been shown to be informative for decoding cognitive processes. Despite the developments in this area, the precision of measures may vary based on the level of noise. Phase distortion due to artefacts and a variety of pre-processing steps that are applied on data, can introduce artificial phase alignment. These artificial phase variations (that is referred to spurious phase variations) are not correlated to any stimulus or event. In a new study, it has been showed that a low instantaneous envelope lead to abrupt changes in IP, which could distort the results of phase synchronization. In this work, we propose a method that is able to estimate the true phase based on the measurements and estimate a standard deviation for the computed phase. The method enables to remove the effect of artificial phase changes due to low envelope. In this approach the analytic signal is modeled by a Kalman smoother, and estimates a more reliable version of the IP from the measurements. At last, we evaluate the model on different synthetic data sets.