Inserm, UMR 1099, Campus de Beaulieu - Bat. 22, Rennes, F-35042, France

Université de Rennes 1, LTSI, Campus de Beaulieu - Bat. 22, Rennes, F-35042, France

Faculty of Mechanical and Electrical Engineering, Al-Baath University, PB 2244, Homs, Syria

CHU de Rennes, Unit, Service de Neurologie, Pôle des Neurosciences Cliniques de Rennes, F-35000, Rennes, France

Abstract

Electroencephalographic (EEG) recordings are often contaminated with muscle artifacts. This disturbing myogenic activity not only strongly affects the visual analysis of EEG, but also most surely impairs the results of EEG signal processing tools such as source localization. This article focuses on the particular context of the contamination epileptic signals (interictal spikes) by muscle artifact, as EEG is a key diagnosis tool for this pathology. In this context, our aim was to compare the ability of two stochastic approaches of blind source separation, namely independent component analysis (ICA) and canonical correlation analysis (CCA), and of two deterministic approaches namely empirical mode decomposition (EMD) and wavelet transform (WT) to remove muscle artifacts from EEG signals. To quantitatively compare the performance of these four algorithms, epileptic spike-like EEG signals were simulated from two different source configurations and artificially contaminated with different levels of real EEG-recorded myogenic activity. The efficiency of CCA, ICA, EMD, and WT to correct the muscular artifact was evaluated both by calculating the normalized mean-squared error between denoised and original signals and by comparing the results of source localization obtained from artifact-free as well as noisy signals, before and after artifact correction. Tests on real data recorded in an epileptic patient are also presented. The results obtained in the context of simulations and real data show that EMD outperformed the three other algorithms for the denoising of data highly contaminated by muscular activity. For less noisy data, and when spikes arose from a single cortical source, the myogenic artifact was best corrected with CCA and ICA. Otherwise when spikes originated from two distinct sources, either EMD or ICA offered the most reliable denoising result for highly noisy data, while WT offered the better denoising result for less noisy data. These results suggest that the performance of muscle artifact correction methods strongly depend on the level of data contamination, and of the source configuration underlying EEG signals. Eventually, some insights into the numerical complexity of these four algorithms are given.

Introduction

Electroencephalographic (EEG) recordings are mandatory for the diagnosis of epilepsy. As part of the presurgical evaluation of drug-resistant epilepsy, long-term Video-EEG recordings are performed. On these traces, transient events called interictal spikes occur between seizures, and convey essential information both to guide further explorations such as intracerebral implantation and to assist surgery. However, epochs of EEG signals containing spikes have to be free of artifacts when both qualitative and quantitative analyses such as source localization are planned.

EEG is unfortunately often contaminated by various physiological activities of non-interest. Among them, muscular or myogenic activity arising from the contraction of head muscles can strongly obscure EEG signals. As recently reviewed in

Therefore, denoising of EEG is a challenging preprocessing step prior to qualitative or quantitative EEG analysis. Minimizing the disturbances due to muscular activity in EEG signals can be considered as a blind source separation (BSS) problem, which consists in estimating the original sources underlying the multi-channel EEG signals, without

In this article, we compare the ability of ICA, CCA, EMD, and WT to remove muscle artifacts from multi-channel EEG data, and to assess their impact on source localization results we chose the Contrast Maximization 2 (CoM2) algorithm

Methods

Problem formulation

The EEG electrical activities recorded at the level of surface electrodes can be considered as an instantaneous linear mixture of elementary sources

where **
x
**

This instantaneous linear model comes from the mathematical formulation of the EEG/MEG forward problem that uses the quasi-static formulation of Maxwell’s equations. Under the quasi-static assumption, the time-derivatives of the associated electric fields are considered as sufficiently small to be ignored in Maxwell’s equations. This means that, for a given position, orientation and spatial extent of the neuronal sources, the resulting electrical activity at the level of surface electrodes is time-independent. Using the Poisson’s equations, the electrical potential can then be computed for each scalp electrode. Under the quasi-static assumption, this potential linearly depends on the current amplitude generated at the level of neuron assemblies or muscles

This article deals with a BSS problem that consists in estimating the source vector **
s
**[

ICA and CCA, as stochastic methods, make the assumption that

**H1:** Spatial statistical independence of sources (i.e., mutual independence of components of

**H2:** Full column rank of the mixing matrix **
A
**;

**H3:** Statistical independence between sources and noise (i.e., independence between components of

In addition, CCA also assumes that

**H4:** Sources are temporally coloured (i.e., statistical dependence between the

On the other hand, in the case of EMD it can be assumed that

**H5:** Each source is the sum of AM–FM modulations. These modulations are different from one to another source.

Finally, in the case of WT, we assume that

**H6:** Each source can be decomposed on a wavelet basis. Admitting that the informative part of a signal is concentrated in few wavelet coefficients having high absolute value, while the noise part is distributed in wavelet coefficients having low absolute value.

In addition to the above-mentioned hypotheses, ICA and CCA also differ from EMD and WT by the way they process the signals. ICA and CCA jointly exploit all electrodes, i.e., they take advantage of all components of **
x
** [

Description of denoising methods

ICA

The concept of ICA was introduced by Herault and Jutten **H1** to **H3**, the goal of ICA is to find a (**
W
**, such that the output signal

is an estimate of the source vector **
s
**

where

CCA

Originally proposed by Hotelling **H2** to **H4**, CCA aims at extracting a **
s
**

where **
y
**

The maximum of **
W
** is called the maximum canonical correlation,

where the eigen-vectors **
W
**.

EMD

EMD was originally introduced in the late 1990s to study water surface wave evolution

In practice, each IMF,

WT

The concept of WT was formalized in early 1980s and, since then, it has extensively been applied in a large variety of fields, such as biomedical signal processing, image compression, astronomy (see, e.g.,

where

Selection of components of interest

For both CoM2 and CCA, the components that represent the sources of interest were selected by calculating the autocorrelation of each component (for a time lag

Regarding the 2T-EMD method, the visual selection of the relevant IMFs is quasi-impossible and an automatic selection of the IMFs of interest is needed. In the past, some interesting EMD procedures have been proposed to automatically select and classify the IMFs of interest. They can be divided into two categories: (i) methods based on low-pass filtering

Signal denoising using DWT requires three successive steps. First, we decompose the original signal by choosing the number of levels

It should be noted that, the number of extracted IMFs (

Computational complexity

In order to evaluate and compare CoM2, CCA, 2T-EMD, and DWT algorithms from a computational complexity point of view, we have calculated the number of floating point operations (flops). A flop corresponds to a multiplication followed by an addition. Although in the usual practice, only multiplications are counted, the order of magnitude of the computational complexity is unchanged, since in most cases, there are roughly as many multiplications as additions. Let

**Algorithms**

**Numerical complexity (Flops)**

CoM2

CCA

2T-EMD

DWT

As an example, the numerical complexity of CoM2, CCA, 2T-EMD, and DWT was calculated on the real data presented in Section 2.6. DWT required the smallest amount of calculation followed by CCA. CoM2 needed larger amount of calculation, while 2T-EMD had the highest computation cost among the four algorithms.

Datasets and performance criteria

Generation of simulated data

To quantitatively evaluate the performance of the four above-mentioned BSS approaches, we simulated 32-channels EEG data, with a spatiotemporal model developed by our team **
S
** containing the time-varying activities of all cortical dipoles of the source space. The

Simulated EEG were generated using a realistic head model representing the brain, the skull and the scalp with a conductivity of each medium fixed to 0.33, 0.0082, and 0.33 S/m, respectively **
A
**. This matrix gives the contribution of each dipole of the mesh at the level of 32 scalp electrode positions (19–20 standard 10–20 electrodes plus additional electrodes at FC1, FC2, FC5, FC6, CP1, CP2, CP5, FT9, FT10, P9, and P10). The spatio-temporal matrix of simulated EEG data is given by

More particularly, for this study two source configurations were considered. In the first configuration, we considered a single patch, made of 100 contiguous triangles (approximately 5 cm²) located in the left superior temporal gyrus. In the second configurations, two patches of 100 triangles each were located in the left superior temporal and left inferior parietal regions, respectively. Activities of dipoles within the patches were highly correlated whereas activities

Performance criteria

Normalized mean-squared error

The performance of CoM2, CCA, 2T-EMD, and DWT was first evaluated by computing the following normalized mean-squared error (NMSE):

where

Effect on source localization

The performances of CoM2, CCA, 2T-EMD, and DWT were also evaluated by examining their impact on source localization results. For this purpose, source localization was performed on original simulated signals (clean data, considered as our reference), on noisy simulated signals at different SNRs, as well as on CoM2, CCA, 2T-EMD, and DWT. We used the recently published 4-ExSo-MUSIC algorithm

Application to real data

In order to test the feasibility of the four denoising algorithms on real data, CCA, CoM2, 2T-EMD, and DWT were applied to the denoising of interictal spikes in a 40-year-old patient (referred as to “Patient P” in the following) suffering from drug-resistant partial epilepsy since the age of 26 years. As part of his presurgical evaluation, Patient P underwent two sessions of video-EEG monitoring, Brain MRI, as well as interictal and ictal SPECT acquisition. During video-EEG monitoring, scalp-EEG data were acquired from 32 electrodes (19–20 standard 10–20 electrodes plus additional electrodes at FC1, FC2, FC5, FC6, CP1, CP2, CP5, FT9, FT10, P9, and P10) at a sampling frequency of 256 Hz with a [0.3–100 Hz] band pass filter. These data were reviewed in order to isolate five different epochs of 2,048 samples (8 s) containing a clean spike, as well as epochs of 2,048 samples including spikes (almost) hidden in muscle activity (at two different levels of noise). The exact same methodology as for simulated data was used to denoise these noisy spikes and reconstruct the denoised EEGs. In addition, the sources of spikes in clean, noisy, and denoised data were estimated using the 4-Exso-MUSIC algorithm.

Results

Results on simulated data

In this section, we report the behavior of CoM2, CCA, 2T-EMD, and DWT algorithms as a function of SNR in noisy simulated data obtained either from a single epileptic patch or from two patches. Examples of simulated, noisy, and denoised data are illustrated in Figure

Example of denoising in the case of simulated data.

**Example of denoising in the case of simulated data.** (Left) Example of the noise-free simulation of EEG data with interictal spike-like activity. These data were generated from the activation of a single patch (5 cm^{2}) located in the superior temporal gyrus. Resulting spikes culminated at electrode T3 (facing the cortical patch). (Right, top) Data after adding real muscle activity (SNR –25 dB) are displayed along with the result of denoising using respectively the CCA, CoM2, 2T-EMD, and DWT algorithms. (Right, bottom) the same noise-free simulation is now displayed after the injection of a lower amount of real muscle activity (SNR –15 dB). The result of denoising for these data is also illustrated.

A visual analysis of denoised data shows that from –25 dB noisy data the spike activity at T3 is well retrieved with CCA and CoM2 although the spike activity slightly diffuses on other channels as compared to original data. On the contrary, 2T-EMD does not retrieve the proper spike amplitude at T3 but does not either increase the diffusion of the spike on remote channels. Using the DWT-based method, the proper spike amplitude at T3 is better retrieved than with 2T-TMD but remains inferior to results obtained with CCA and CoM2. Furthermore, other channels are less denoised with the DWT than with 2T-EMD, CCA, or CoM2. Regarding –15 dB noisy data, in which spikes are not entirely hidden by muscle activity, CCA and CoM2 denoised data are very similar to the original simulated data. In that case, the 2T-EMD and DWT algorithms are not denoising data as well as the two other algorithms.

NMSE

For data simulated from a single epileptic patch (Figure

Performance of denoising methods in the case of data generated from a single source.

**Performance of denoising methods in the case of data generated from a single source.** The mean performance (NMSE) over the 50 simulation trials, of the three denoising methods CCA, CoM2, 2T-EMD, and DWT is plotted for different SNR values. This criteria is calculated either for all electrodes (top) or for the single electrode (T3) facing the cortical patch, i.e., where the maximal spike amplitude is detected (bottom).

The results obtained on signals simulated from two epileptic patches are illustrated in Figure

Performance of the denoising methods in the case of data generated from two distinct sources.

**Performance of the denoising methods in the case of data generated from two distinct sources.** The mean performance (NMSE) over the 50 simulation trials of the three denoising methods CCA, CoM2, 2T-EMD, and DWT is plotted for different SNR values. This criteria is calculated either for all electrodes (top) or for the two electrodes (respectively T3 and CP5) facing the two cortical patches.

Figures

Source localization

As another performance criterion, source localization was applied on original and noisy simulated data before and after denoising by the CCA, CoM2, 2T-EMD, or the DWT algorithms. An example is given in Figure

Estimation of sources of denoised simulated data using 4-ExSo-MUSIC.

**Estimation of sources of denoised simulated data using 4-ExSo-MUSIC.** An example for data simulated both from a single or from two distinct sources is systematically displayed next to each other for a given set of original, noisy, or denoised data. Brown: real patch; purple: truly estimated part of the patch; Orange: falsely estimated part of the patch.

ROC curves obtained after source localization on a set of 50 original, noisy (with different SNR values), and corresponding denoised trials.

**ROC curves obtained after source localization on a set of 50 original, noisy (with different SNR values), and corresponding denoised trials.** These data are obtained after localizing EEG spikes simulated from either a single patch configuration **(a)** or from two distinct patches **(b)**. TPF: true positive fraction; FPF: false positive fraction.

ROC curves show that this trend is reversed for higher SNR values (Figure

Similarly, in the double-patch configuration, and for low SNR data (–25 dB), spikes arising from two distinct patches are also better localized after 2T-EMD than after CCA, CoM2, and DWT (see Figure

Results on real data

In the absence of any perturbation by muscle activity, spikes of Patient P were localized in the lateral anterior temporal region (Figure

Performance of the four different algorithms on real EEG data (8s) recorded in an epileptic patient during the interictal period.

**Performance of the four different algorithms on real EEG data (8s) recorded in an epileptic patient during the interictal period:****(a)** One example of a typical noise-free interictal spike culminating at FT10. **(b)** A first 8s-epoch of data contaminated with muscle activity and the corresponding EEGs reconstructed after CCA, CoM2, 2T-EMD, and DWT. **(c)** A second 8s-epoch of data contaminated with muscle activity and the corresponding EEGs reconstructed after CCA, CoM2, 2T-EMD, and DWT. The results of source localization using 4-ExSo-MUSIC are represented at the bottom of each epoch of clean, noisy or denoised EEG.

For both sets of noisy epochs the source of spike was mislocalized in the right inferior frontal region (Figure

Discussion

Muscle artifacts are a major source of contamination of scalp EEG data. As a result a rapid and reliable denoising of these data constitutes an essential issue particularly when these signals are used for diagnosis, which is the case in patients with epilepsy. Moreover, artifact correction is crucial when the EEG will be further analyzed with signal processing tools, such as source localization.

In this article, we compared the ability of two stochastic BSS approaches (CoM2 and CCA) and of two deterministic methods (2T-EMD and DWT) to remove muscle artifacts from EEG signals. Our results showed unequal performances of the four algorithms according to the level of SNR and according to the source configuration (single patch versus two patches). At very low SNR and when a single source was used to simulate epileptic spikes, 2T-EMD offered the best results as compared to the other considered approaches. Indeed, for these low SNR, CoM2 and CCA tend to exaggerate the contribution of the source to the scalp EEG activity at the level remote channels. This most likely explains why for these two algorithms, the performance averaged over all channels is low for very low SNR while the performance calculated at T3 is high for all SNR considered. On the contrary, 2T-EMD did not overspread the source activity at distant electrodes but rather reduced the contribution of the source at the electrode facing the source. However, for higher SNR values, this trend was reversed. The performance of 2T-EMD slightly improved while CoM2 and CCA retrieved the signal in a much proper way than for very low SNR, with less spreading at the level of distant channels. Expectedly, for higher levels of SNR, source localization gave more reliable results when applied to CCA- or CoM2-denoised data than when applied to 2T-EMD-denoised data. The worse behavior of the DWT for at very low SNR is explained by the fact that for this cases the wavelet coefficients of epileptic spikes have small values, comparable to noise and artifacts, especially for electrodes located far from the epileptic patch, and even the use of an algorithm with low thresholding as SURE do not remove all the noise and slightly corrupt the signal of interest, namely the epileptic spikes.

Similar conclusions could be derived when two distinct patches are used to simulate epileptic spikes. Very low SNR data were more accurately denoised by 2T-EMD than by CCA, CoM2, or DWT. In particular, both spike activities visible at the electrodes facing the two patches (T3 and CP5, respectively) were retrieved after 2T-EMD denoising, and subsequently, two distinct sources could be estimated from these denoised data. Regarding the DWT, because this method is used, in a monovariate way (i.e., channel per channel) the difficulties raised in the case of two distinct patches are exactly the same than those retrieved when single source was used to simulate epileptic spikes (single patch). Regarding, CCA or CoM2 (although to a lesser extend) retrieved the two distinct sources with more difficulty and extracted both sources in one component. As a result, spike activities were mixed at the level of the reconstructed scalp EEG. Source localization in that case provided misleading results with the source being estimated between the two patches. For higher SNR, this difficulty persisted for CCA while the performance of CoM2 slightly improved. This result might be explained by the fact that CoM2 exploits more statistical information from the signal (second and FO cumulants) than CCA (second-order cumulants). It is noteworthy that in another study the CCA approach was shown to provide better results, in terms of NMSE, than an ICA-based method

The number of electrodes is a crucial aspect that should be considered to explain the efficiency of BSS methods. In particular, the weak performance of CCA or CoM2 in our study with respect to low SNR data (or high SNR data due to the activation of two cortical regions) is most likely due to an insufficient number of electrodes. In these situations, the number of sources is probably higher than the number of electrodes which leads to an underdetermined mixture and consequently to the well-known ill-posed inverse problem. Consequently, when a small number of electrodes is used, the methods extract a linear combination of sources belonging to the same subspace instead of estimating the sources themselves.

Despite the above-mentioned differences observed between the four algorithms, the denoising process has clearly improved the results of sources localization. With this respect, the results are in harmony with those of a recent and important study showing the usefulness of applying ICA/CCA denoising techniques to ictal EEG signals in order to localize the epileptic zones

This simulation study globally corroborated the results obtained with real data and aided in their interpretation. As for simulations, the source of spikes is mislocalized when unprocessed and noisy data are used. Moreover, in the case of the first set of noisy data (#1), the source localized from denoised data is consistent with the source localized from clean data, in a comparable way whatever the method used for artifact removal. According to simulations, this behavior suggests that noisy data #1 are moderately contaminated by muscle activity. In the second case, the source estimated from 2T-EMD-denoised data is clearly more consistent with that of clean data than when source localization is performed on CCA or CoM2 denoising. This is consistent with the results obtained in the case of very low SNR simulations, and suggests that data set #2 is strongly affected by muscle activity. Interestingly, for these data, the source localization result obtained from DWT is equivalent to the one provided by 2T-EMD, even if the EEG signals denoising seems visually less effective than for the three other algorithms. Note also that, for these data, the source estimated after CoM2-denoising is partly consistent with the source of clean data, but extends beyond it, whereas CCA-denoised spikes give raise to a source inconsistently localized in the mesio-temporal region. In these two cases, it is difficult to rule out the possibility that spikes may actually arise from the right mesial temporal region or may spread to the right insula. Nevertheless, in the absence of concomitant depth recordings, this question cannot easily be answered.

Conclusion

In general, our results obtained both in the context of simulated and real interictal epileptic spikes suggest that 2T-EMD should be preferred for the denoising of low SNR data but that the reconstructed data would most likely lead too (small) localization errors. This agrees with a recent study showing that EMD outperforms ICA in the context of low SNR simulated data

It is worth mentioning that these conclusions hold in the case of interictal EEG spikes. Since our study demonstrates that the performance of muscle artifact correction methods significantly depend on the level of data contamination, and of the source configuration underlying EEG signals, the four algorithms may also perform differently on other type of data. In particular, further work should consider signals at the onset of epileptic seizures, as these signals directly relate to the epileptogenic zone, and are often obscured by muscle activity.

Competing interests

The authors declare that they have no competing interests.