Low-Density EEG for Neural Activity Reconstruction Using Multivariate Empirical Mode Decomposition

Abstract

Several approaches can be used to estimate neural activity. The main differences between them concern the a priori information used and its sensitivity to high noise levels. Empirical mode decomposition (EMD) has been recently applied to electroencephalography EEG-based neural activity reconstruction to provide a priori time-frequency information to improve the estimation of neural activity. EMD has the specific ability to identify independent oscillatory modes in non-stationary signals with multiple oscillatory components. However, attempts to use EMD in EEG analysis have not yet provided optimal reconstructions, due to the intrinsic mode-mixing problem of EMD. Several studies have used single-channel analysis, whereas others have used multiple-channel analysis for other applications. Here, we present the results of multiple-channel analysis using multivariate empirical mode decomposition (MEMD) to reduce the mode-mixing problem and provide useful a priori time-frequency information for the reconstruction of neuronal activity using several low-density EEG electrode montages. The methods were evaluated using real and synthetic EEG data, in which the reconstructions were performed using the multiple sparse priors (MSP) algorithm with EEG electrode montages of 32, 16, and 8 electrodes. The quality of the source reconstruction was assessed using the Wasserstein metric. A comparison of the solutions without pre-processing and those after applying MEMD showed the source reconstructions to be improved using MEMD as a priori information for the low-density montages of 8 and 16 electrodes. The mean source reconstruction error on a real EEG dataset was reduced by 59.42 and 66.04% for the 8 and 16 electrode montages, respectively, and that on a simulated EEG with three active sources, by 87.31 and 31.45% for the same electrode montages.

Analysis in the frequency domain of multicomponent oscillatory modes of the human electroencephalogram extracted with multivariate empirical mode decomposition

“…These findings are the evidence of one of the limitations of the empirical mode decomposition: the so called mode-mixing, consisting in the appearance of disparate scales in an IMF, or when a signal with a similar scale appears in different IMF components. This fact has been reported and multiple procedures have been proposed to mitigate its effect (Munoz-Gutierrez et al 2018;Soler et al 2020;Tsai et al 2016;Zheng, Xu 2019).…”

“…The EMD method that was applied to decompose the EEG was the most novel of the multivariate versions, the APIT-MEMD (Hemakom et al 2016) that has been developed as an improvement to the MEMD Ur Rehman et al 2010), with the express purpose to cope with power imbalances and inter-channel correlations of multichannel signals as the EEG signal, and also was used the method proposed by (Xie, Wang 2006) for the calculation of the mean spectral frequencies that mitigate the effect of some frequencies that have associated low values of power spectral density. However, as has been acknowledged by other authors the mode-mixing problem continues to be a big issue for the analysis of multichannel signals like the EEG (Alegre-Cortes et al 2016;Munoz-Gutierrez et al 2018;Soler et al 2020;Zheng, Xu 2019).…”

“…Some authors have recently suggested that the first IMFs decomposed from the EEG using the multivariate empirical mode decomposition could be associated to classical EEG bands (Noshadi et al 2014;Schiecke et al 2019;Soler et al 2020;Tsai et al 2016). The IMF1 would correspond to the gamma band, the IMF2 to the beta, the IMF3 to the alpha, the IMF4 to the theta, and the IMF5 and IMF6 would be sub-bands of the delta band (Tsai et al 2016).…”

“…A cardinal tool to the study of brain rhythms was the development of the FFT algorithm (Cooley, Tukey 1965) that was incorporated to the spectral analysis of the EEG and continues to be used nowadays with several improvements. However, the EEG dynamics shows nonlinearity and non-stationarity (Noshadi et al 2014;Abdulhay et al 2017;Alegre-Cortes et al 2016;Soler et al 2020) and strictly speaking, the FFT methods are limited to the study of linear systems. Therefore, in some conditions, the interpretation of the results obtained through the FFT could be meaningless.…”

Comparison between traditional FFT and marginal spectra using the Hilbert-Huang transform method for the broadband spectral analysis of the EEG in healthy humans

“…Nonparametric methods that apply the fast Fourier transform (FFT), have been the main tool to obtain the spectra from which calculate the indices in the frequency domain of the EEG. However, the EEG dynamics shows nonlinearity and non-stationarity (Noshadi et al 2014;Abdulhay et al 2017;Alegre-Cortes et al 2016;Soler et al 2020) and strictly speaking, the FFT methods are limited to linear systems. Therefore, in some conditions the interpretation of the results obtained through the FFT can be meaningless.…”