Outlier detection and removal in multifractal analysis of electrophysiological brain signals

Abstract The analysis of the scale-invariant properties of brain activity has received growing attention in the last 15 years, especially in the context of the brain criticality hypothesis. Multifractal analysis (MFA) extends the ability of the usual tools in brain criticality research (e.g., detrended fluctuation analysis) to characterize scale invariance or scale-free dynamics by investigating the scaling properties of statistical moments beyond second-order analysis. However, MFA is very sensitive to the presence of outliers in the recorded time series, for instance, in the form of impulsive noise. In this work, we propose a novel algorithm for outlier detection and removal, which relies on the wavelet p -leader MFA formalism. The proposed approach consists in temporally segmenting the time-scale representation of the data (time series), and then tagging and removing the outlier segments from the final MFA estimation process. We first compare on synthetic noisy mono- and multifractal time series the performances of our method with those of existing techniques such as the wavelet p -leader MFA formalism and a naive robust cumulant-based approach. As a proof of concept, the proposed method is then evaluated on a single noisy resting-state magnetoencephalography (MEG) recording of a healthy volunteer. Overall, our results show that in the presence of noise impulses, this method removes the existing bias with standard MFA tools (wavelet leader-based analysis) on both synthetic and neurophysiological signals, with consistent findings across the two brain hemispheres in MEG.