A New Statistical Model of Electroencephalogram Noise Spectra for Real-time Brain-Computer Interfaces

TL;DR

This paper introduces a novel EEG noise model called GVZM PSD that accurately captures background brain activity with few parameters, improving real-time BCI frequency estimation accuracy.

Contribution

The paper proposes the GVZM PSD model for EEG noise, validated through theoretical derivations, simulation, and real-time algorithms, offering a new paradigm for EEG signal processing.

Findings

GVZM PSD matches EEG PSDs from 0 to over 30 Hz with high accuracy.

GVZM-based algorithms outperform existing SSVEP estimators statistically.

The model provides a reliable technique for EEG noise understanding and management.

Abstract

$Objective$: A characteristic of neurological signal processing is high levels of noise from sub-cellular ion channels up to whole-brain processes. In this paper, we propose a new model of electroencephalogram (EEG) background periodograms, based on a family of functions which we call generalized van der Ziel--McWhorter (GVZM) power spectral densities (PSDs). To the best of our knowledge, the GVZM PSD function is the only EEG noise model which has relatively few parameters, matches recorded EEG PSD's with high accuracy from 0 Hz to over 30 Hz, and has approximately $1/f^\theta$ behavior in the mid-frequencies without infinities. $Methods$: We validate this model using three approaches. First, we show how GVZM PSDs can arise in population of ion channels in maximum entropy equilibrium. Second, we present a class of mixed autoregressive models, which simulate brain background noise and whose periodograms are asymptotic to the GVZM PSD. Third, we present two real-time estimation algorithms for steady-state visual evoked potential (SSVEP) frequencies, and analyze their performance statistically. $Results$: In pairwise comparisons, the GVZM-based algorithms showed statistically significant accuracy improvement over two well-known and widely-used SSVEP estimators. $Conclusion$: The GVZM noise model can be a useful and reliable technique for EEG signal processing. $Significance$: Understanding EEG noise is essential for EEG-based neurology and applications such as real-time brain-computer interfaces (BCIs), which must make accurate control decisions from very short data epochs. The GVZM approach represents a successful new paradigm for understanding and managing this neurological noise.