The WQN algorithm for EEG artifact removal in the absence of scale invariance

TL;DR

This paper investigates EEG signal scaling behavior, showing lack of scale invariance in certain brain states, and introduces the wavelet quantile normalization (WQN) algorithm for artifact removal that operates independently at each scale.

Contribution

It develops a theoretical framework for the WQN algorithm's regularization properties and demonstrates its effectiveness and basis-independence in real-time EEG artifact correction.

Findings

WQN can eliminate artifacts without relying on scale invariance.

The algorithm's performance is basis-independent.

WQN exhibits non-local effects on wavelet coefficients.

Abstract

Electroencephalogram (EEG) signals reflect brain activity across different brain states, characterized by distinct frequency distributions. Through multifractal analysis tools, we investigate the scaling behaviour of different classes of EEG signals and artifacts. We show that brain states associated to sleep and general anaesthesia are not in general characterized by scale invariance. The lack of scale invariance motivates the development of artifact removal algorithms capable of operating independently at each scale. We examine here the properties of the wavelet quantile normalization algorithm, a recently introduced adaptive method for real-time correction of transient artifacts in EEG signals. We establish general results regarding the regularization properties of the WQN algorithm, showing how it can eliminate singularities introduced by artefacts, and we compare it to traditional thresholding algorithms. Furthermore, we show that the algorithm performance is independent of the wavelet basis. We finally examine its continuity and boundedness properties and illustrate its distinctive non-local action on the wavelet coefficients through pathological examples.