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.

The localization of active brain sources from Electroencephalogram (EEG) is a useful method in clinical applications, such as the study of localized epilepsy, evoked-related-potentials, and attention deficit/hyperactivity disorder. The distributed-source model is a common method to estimate neural activity in the brain. The location and amplitude of each active source are estimated by solving the inverse problem by regularization or using Bayesian methods with spatio-temporal constraints. Frequency and spatio-temporal constraints improve the quality of the reconstructed neural activity. However, separation into frequency bands is beneficial when the relevant information is in specific sub-bands. We improved frequency-band identification and preserved good temporal resolution using EEG pre-processing techniques with good frequency band separation and temporal resolution properties. The identified frequency bands were included as constraints in the solution of the inverse problem by decomposing the EEG signals into frequency bands through various methods that offer good frequency and temporal resolution, such as empirical mode decomposition (EMD) and wavelet transform (WT). We present a comparative analysis of the accuracy of brain-source reconstruction using these techniques. The accuracy of the spatial reconstruction was assessed using the Wasserstein metric for real and simulated signals. We approached the mode-mixing problem, inherent to EMD, by exploring three variants of EMD: masking EMD, Ensemble-EMD (EEMD), and multivariate EMD (MEMD). The results of the spatio-temporal brain source reconstruction using these techniques show that masking EMD and MEMD can largely mitigate the mode-mixing problem and achieve a good spatio-temporal reconstruction of the active sources. Masking EMD and EEMD achieved better reconstruction than standard EMD, Multiple Sparse Priors, or wavelet packet decomposition when EMD was used as a pre-processing tool for the spatial reconstruction (averaged over time) of the brain sources. The spatial resolution obtained using all three EMD variants was substantially better than the use of EMD alone, as the mode-mixing problem was mitigated, particularly with masking EMD and EEMD. These findings encourage further exploration into the use of EMD-based pre-processing, the mode-mixing problem, and its impact on the accuracy of brain source activity reconstruction.

Several approaches can be used for estimating neural activity. The main differences between them are in the apriori information used and their sensibility to high noise levels. Empirical Mode Decomposition (EMD) has been recently applied to Electroencephalography EEG-based neural activity reconstruction to provide apriori time-frequency information to improve the neural activity estimation. EMD has the specific ability to identify independent oscillatory modes in non-stationary signals with multiple oscillatory components. The various attempts to use EMD in EEG analysis, however, did not provide yet the best reconstructions due to the intrinsic mode mixing problem of EMD. Some previous works have used a single-channel analysis and in other cases, multiple-channel have been used for other applications. In this paper, we present a study about multiplechannel analysis using Multivariate Empirical Mode Decomposition (MEMD) as a method to attenuate the mode mixing problem and to provide apriori useful time-frequency information to the reconstruction of neuronal activity using several low-density EEG electrode montages.The methods were evaluated over real and synthetic EEG data, in which the reconstructions were performed using multiple sparse priors (MSP) method with several electrode numbers of 32, 16, and 8, and the source reconstruction quality was measured using the Wasserstein Metric. Comparing the solutions when no pre-processing was made and when MEMD was applied, the source reconstructions were improved using MEMD as apriori information in the low-density montage of 8 and 16 electrodes. The mean source reconstruction error on a real EEG dataset was reduced a 59.42% and 66.04% for the 8 and 16 electrodes montages respectively, and on a simulated EEG with three active sources, the mean error was reduced an 87.31% and 31.45% for the same electrodes montages.