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Noiseassisted multivariate empirical mode decomposition for multichannel EMG signals
BioMedical Engineering OnLine volume 16, Article number: 107 (2017)
Abstract
Background
Ensemble Empirical Mode Decomposition (EEMD) has been popularised for singlechannel Electromyography (EMG) signal processing as it can effectively extract the temporal information of the EMG time series. However, few papers examine the temporal and spatial characteristics across multiple muscle groups in relation to multichannel EMG signals.
Experiment
The experimental data was obtained from the Center for Machine Learning and Intelligent Systems, University of California Irvine (UCI). The data was donated by the Nueva Granada Military University and the Technopark node Manizales in Colombia. The databases of 11 male subjects from the healthy group were taken into the study. The subjects undergo three exercise programs, leg extension from a sitting position (sitting), flexion of the leg up (standing), and gait (walking), while four electrodes were placed on biceps femoris (BF), vastus medialis (VM), rectus femoris (RF), and semitendinosus (ST).
Methods
Based on the experimental data, a comparative study is provided by assessing the Empirical Mode Decomposition (EMD)based approaches, EEMD, Multivariate EMD (MEMD), and NoiseAssisted MEMD (NAMEMD). The outcomes from these approaches are then quantitatively estimated on the basis of three criterions, the number of Intrinsic Mode Functions (IMFs), modealignment and modemixing.
Results
Both MEMD and NAMEMD methods (except EEMD) can guarantee equal numbers of IMFs. For modealignment and modemixing, NAMEMD is optimal compared with MEMD and EEMD, and MEMD is merely better than EEMD.
Conclusions
This study proposes the NAMEMD approach for multichannel EMG signal processing. This finding implies that NAMEMD is effective for simultaneously analysing IMFs based frequency bands. It has a vital clinical implication in exploring the neuromuscular patterns that enable the multiple muscle groups to coordinate while performing the functional activities of daily living.
Background
Electromyography (EMG) is the collective electric manifestation during muscle contraction, and indicates the electrophysiological responses of motor units from a muscle group, which is controlled by the nervous system. The surface EMG signal, originating in motor units and then recorded by measurement tools, was often contaminated by various types of noises or artifacts, e.g., power line interference, baseline wandering, electrocardiographic (ECG) artifacts, capacitive effects of the detection site, and the firing rate of motor units [1,2,3,4,5,6]. Therefore, the identity of an actual EMG still remains difficult [7,8,9].
Recently, several methods have been developed to analyse and denoise the EMG signal [10,11,12]. The conventional techniques based on Fourier analysis (e.g., IIR filters) are widely used for EMGbased filtering. However, Fourier analysis is purely based on predefined basis functions, which not only reduces the noise but also attenuate the EMG signal. As an alternative to the usual Fourier transform method, wavelet analysis is also popularised due to its advantages in terms of the time–frequency representation [13,14,15,16]. The waveletbased approaches, however, are also suboptimal because the preselected wavelet function is often not suitable for matching the natural property of an EMG signal. Previous studies have also introduced the Empirical Mode Decomposition (EMD) approach to handle EMG signals [17]. Instead of those reported in literatures [18], the EMD is a fully datadriven adaptive time–frequency analysis method, and offers no prior assumption through the overall data processing procedure [19,20,21,22].
The EMD algorithm was put forward by Huang et al. and provided the most successful results for the decomposition and time–frequency analysis of nonstationary signals. It is given as a sifting process that decomposes a signal into a finite set of intrinsic mode functions (IMFs), amplitude and/or frequencymodulated components representing its inherent oscillatory modes. Adriano et al. first employed this technique to filter EMG signals in background activity attenuation [17]. However, the first version of EMD was only used for a singlechannel EMG, and did not focus on the accuracy of the decomposed subfrequency bands. In order to alleviate this problem, the Ensemble EMD (EEMD), an adaptive dyadic filter bank, was introduced. This method can effectively eliminate the modemixing and physically produce more unique frequency levels. The literature shows that several studies have investigated the denoising performance for EMG signals using the EEMD algorithm [23]. However, such singlechannel based EMD algorithms cannot be directly applied into the multiplechannel EMG signal processing [24]. Moreover, the EMD or EEMD algorithms cannot guarantee the equality of the number of decomposed IMFs across multichannels, and may lead to subsequent EMGbased analyses being physically meaningless. Accordingly, the multivariate extension of EMD (MEMD) and its noiseassisted analysis method, NoiseAssisted Multivariate EMD (NAMEMD) have been developed recently to produce the same number of IMFs across all channels thereby facilitating direct multichannel analyses with the consideration of crosschannel interdependence (modealignment) and singlechannel independence (modemixing) [25,26,27,28,29,30].
EEMD has been extensively applied as an accurate and computationally efficient quantitative analysis for electromyography (EMG) signals. The EEMD algorithm can effectively extract the temporal information of EMG time series. However, few papers examine the temporal and spatial characteristics across multiple muscle groups in relation to multichannel EMG signals. In this study, NAMEMD is proposed to handle the multichannel EMG signal processing. The performance of the proposed method has been validated by comparing it with EEMD and MEMD. The experimental data was obtained from the Center for Machine Learning and Intelligent Systems, University of California Irvine (UCI). The data was donated by the Nueva Granada Military University and the Technopark node Manizales in Colombia. Three criterions are proposed to assess the decomposition performance, (1) the number of intrinsic mode functions; (2) modealignment (common frequency scales in the same indexed IMFs across different channels) for the crosschannel interdependence; (3) modemixing (a single IMF containing multiple scales and/or a single scale residing in multiple IMFs) for the singlechannel independence. Results indicate that both MEMD and NAMEMD methods (except EEMD) can guarantee equal numbers of IMFs. Specifically, for modealignment and modemixing, NAMEMD is optimal compared to MEMD and EEMD, and MEMD is merely better than EEMD.
Experiments
The experimental data was obtained from the Center for Machine Learning and Intelligent Systems, University of California Irvine (UCI). The data was donated by the Nueva Granada Military University and the Technopark node Manizales in Colombia. UCI consented to cite these datasets in publications [31]. This work is also approved by the Institution Research Ethics Board of University of Electronic Science and Technology of China (UESTC). The databases of 11 male subjects from the healthy group are taken into the study. The subjects undergo three exercise programs associated with the knee joint, leg extension from a sitting position (sitting), flexion of the leg up (standing), and gait (walking), while four electrodes are placed on biceps femoris (BF), vastus medialis (VM), rectus femoris (RF), and semitendinosus (ST). The goniometer is also used to record the angle of the knee joint during the exercise programs. Each subject is asked to perform these exercise programs once, and each exercise program contains approximately five motion repetitions. The period time of motion is about 4 s, 2 s for motion and 2 s for rest.
Methods
EEMD
The Empirical Mode Decomposition (EMD) is a fully datadriven and adaptive time–frequency analysis method. It describes a signal as a linear combination of a finite set of intrinsic mode functions (IMFs) and a residual signal. The mathematic representation of EMD can be depicted as
where x(t) is an original signal, \(c_m(t)\) and r(t) represent the \(m^{th}\) IMF and the residual assumed as the \((M+1)^{th}\) IMF, respectively. These resultant IMFs, \({c_m(t)}^M_{m=1}\), are sequentially extracted from the original signal by an iteration algorithm called the sifting processing [19]. For the EMDbased sifting process, the local maxima and minima of x(t) are first identified, and the upper (lower) envelope is constructed by fitting the local maxima (minima) into a cubicspline curve. The averaged curve of upper and lower envelopes is then intended to update x(t) by subtracting it from x(t). This sifting process will be iteratively executed until each IMF can be determined, while two stoppage criterions should be satisfied, i.e., (a) the number of zero crossings and the number of extrema (inclusive of the total number of the local maxima and minima) should not differ by more than one; (b) the average value of the upper envelope and the lower envelope through the overall data should be zero. After repeating the above sifting process, all IMFs \({c_m(t)}^M_{m=1}\) are obtained when the residual r(t) becomes a monotonic function.
For EEMD, the extra white Gaussian noises (WGNs) w(t) are added with the original signal x(t) to obtain an ensemble of noiseassisted signal s(t), i.e., \(s(t)=x(t)+w(t)\), and the ensemble signal is decomposed by using the EMD algorithm. This single noiseadded procedure is then repeatedly executed, and for each iteration the different realization of white noise \(w_n (t)\) is given where \(n=1,2,\ldots N\) representing the number of iterations that is set to 50 in this study. The final IMFs can be calculated by averaging the same indexed IMFs of the decomposition. The EEMD algorithm is provided as follows [29]:

(1)
Input signal, x(t);

(2)
Generate \(\bar{x}_n(t)= x(t) + w_n(t)\) for \(n=1,2,\ldots N\), where \(w_n(t)\) (\(n=1,2,\ldots N\)) are N different realizations of WGN;

(3)
Identify all local extrema of \(\bar{x}_n(t)\);

(4)
Find lower and upper envelopes, \(e_l^n (t)\) and \(e_u^n (t)\), which interpolate all local minima and maxima, respectively;

(5)
Calculate the local mean, \(\bar{m}^n(t) = \frac{1}{2}(e_l^n(t)+ e_u^n(t))\);

(6)
Subtract the local mean from \(\bar{x}_n(t)\), \(c_m^n(t)=\bar{x}_n(t)\bar{m}^n(t)\) (n is the index number of IMF);

(7)
Let \(\bar{x}_n(t)=c_m^n(t)\) and go to step 3); repeat until \(c_m^n (t)\) becomes IMFs;

(8)
Average the corresponding IMFs from the whole ensemble to obtain the averaged IMFs; for instance, the \(m^{th}\) IMF can be obtained by using \(\bar{c}_m(t)=\frac{1}{N}(\sum _{n=1}^N c_m^n(t))\).
MEMD
Rehman and Mandic developed multivariate empirical mode decomposition (MEMD), which is a natural extension of the original EMD/EEMD. In MEMD, the multiplechannel EMGs should be first projected into ndimensional spaces based on low discrepancy Hammersley sequence. The projections along different directions in multidimensional spaces represent the amplitudes of EMGs across four channels. The extrema are interpolated via cubicspline interpolation in order to obtain the subenvelopes \({e_{\theta _v}(t)}_{v=1}^V\). Those subenvelopes are then averaged to obtain a local mean of a multiplechannel EMG signal, M(t). Then, the first IMF can be extracted by subtracting the local mean from the input channels. The outline of MEMD algorithm is presented as follows [25]:

(1)
Choose a suitable point set for sampling a \((p1)\) sphere;

(2)
Calculate a projection, \(w_{\theta _v}(t)\), of Nchannel input signals \(x^N(t)\) (N = 4) along the direction vector \(d_{\theta _v}\), for all v (the whole set of direction vectors), giving \({w_{\theta _v}(t)}^V_{v=1}\) as the set of projections;

(3)
Find the time instant \({t_{\theta _v}(t)}^V_{v=1}\) corresponding to the maxima of the set of projected signal \({w_{\theta _v}(t)}^V_{v=1}\);

(4)
Interpolate \([t_{\theta _v}(t),x^N(t_{\theta _v})]\) to obtain multivariate envelope curve \({e_{\theta _v}(t)}^V_{v=1}\);

(5)
For a set of V direction vectors, the mean M(t) of the envelope curve is computed as \(M(t)=\frac{1}{V}(\sum _{v=1}^V e_{\theta _v}(t))\);

(6)
Let \(c^N(t)= x^N(t)M(t)\). If \(c^N(t)\) fulfills the stopping criterion for a multivariate IMFs, apply the above procedure to \(x^N(t)c^N(t)\); otherwise, apply it to \(c^N(t)\).
Different with EEMD, the sifting process is followed by
where e(t) is the bias function defined by \(e(t)=\frac{1}{N}\sum _{n1}^N\mid c^n(t)M(t)\mid\), and the threshold value \(\gamma\) was set to 0.2 based on the EMG signals during lowerlimb exercises. The sifting process will be continued if Eq. (2) is satisfied.
NAMEMD
The NoiseAssisted multivariate empirical mode decomposition (NAMEMD) was also introduced by Rehman and Mandic. This signal processing work exploits the dyadic filter properties of EMD and MEMD. Additionally, it also applies the noise assisted analysis method into MEMD, a dyadic filter bank on each channel while adding certain multidimensional WGNs together with the original signals which are decomposed by using MEMD. More specifically, Kchannel (\(K \ge 1\)) uncorrelated WGNs time series of the same length with that of the Mchannel EMGs (\(M = 4\)) are randomly separately created. Then, a new input multichannel signal is constructed by adding the original EMGs with the noise channel, the resulting \((M+K)channel\) multivariate signal. Considering the decomposition of the constructed signal, the remaining procedures are strictly followed by those of MEMD [32]. Figure 3 outlines the processing procedure of NAMEMD. The effects of the number of noise channels and noise power in NAMEMD are discussed in [33]. In this study, the average STD based on all EMG channels is selected as the residual noise power, and the number of noise channel is set to four. The schematic diagram for methods of EEMD, MEMD, and NAMEMD is presented in Fig. 1.
Data preprocessing and evaluation criterions
Data preprocessing
The raw EMG data measured from each subject were first segmented. The period of the exercise motion was reserved and labeled. The approaches of EEMD, MEMD, and NAMEMD are then used to decompose these segmented EMG data, by which the decomposed IMFs are obtained via three methods, and then normalized by using standard deviation. Based on each single normalized IMF data, the alignment of IMF based frequency bands in cases of EEMD, MEMD, and NAMEMD is estimated by the spectra analysis. The last step is to evaluate three criterions, the number of IMFs (indicating crosschannel interdependence), modealignment (estimating the alignment of the frequency bands of the sameindex IMFs across channels), and modemixing (estimating the similarity of the frequency bands of IMFs within a single channel). Figure 2 depicts the schematics for data flow and evaluation criterions, the number of IMFs, modealignment, and modemixing.
Modealignment
The modealignment effect indicates the common frequency scales in the same indexed IMFs across different channels. This effect would numerically analyse the correlations of frequency scales for each component of the EMG channels, and take advantages of comparatively analysing the frequency similarity of the sameindexed IMFs across channels. In order to obtain this performance, the power spectral density (PSD) of the normalized IMF is first calculated. The PSD correlations between two IMFs are then obtained by \(c_{i,j}\), where i stands for the ith indexed IMF, and j is for the number of the channel. The correlation matrix for all IMFs across channels could be expressed as
The elements in the ith row of the correlation matrix are averaged to represent the modealignment value in the ith indexed IMF.
Modemixing
The modemixing effect describes the overlap of frequency information among the decomposed IMFs within one EMG channel, which would reflect whether or not a single IMF contains multiple scales and/or a single scale resides in multiple IMFs [34]. In this study, we used the following equation to quantitatively describe the modemixing effects, \(MM_{i,j}\),
where \(f_{2i}\), \(f_{8i}\), and \(D_i\) are the PSD of the ith indexed IMF. \(f_2\), \(f_8\) are the frequencies at which 20 and 80% of the energy of an IMF are reached, respectively. \(D_i\) is the difference between \(f_{2i}\) and \(f_{8i}\). Based on Eq. (4), the modemixing effect for a single EMG channel could be calculated as
where I is the total number of IMFs.
Results
Figure 3 shows an example of the decomposition result in the vastus medialis muscle group for three exercise programs (sitting, standing, and walking) for EEMD, MEMD and NAMEMD. Since the most predominant energy for an EMG signal is approximately between 20 and 500 Hz [5], the decomposed components that have lower subfrequency bands than 20 Hz are synthesized together (from the 5th to 11th IMFs, the 6th to 16th IMFs, and the 7th to 16th IMFs for EEMD, MEMD, and NAMEMD, respectively).
Spectra analysis
In order to analyse IMF based frequency components produced by EEMD, MEMD, and NAMEMD, the decomposed IMFs, specifically representing one of exercise motions, are first normalized. These IMFs are then utilized for the analysis of spectra. Figure 4 indicates the spectra results of IMFs for three exercise motions decomposed by EEMD, MEMD, and NAMEMD. In this study, we only focus on the shape of individual spectra in considerations of modealignment and modemixing. The alignment of frequency bands of the sameindex IMFs in muscles BF, VM, RF, and ST is closer, the modealignment performance is more prominent. The spectra figures only can qualitatively analyze and demonstrate the differences of decomposition by EEMD, MEMD, and NAMEMD, in which the stabilization of the shape of individual spectra from BF, VM, RF and ST can be observed. Based on these spectra information, the statistical analyses are used to quantitatively estimate the performance of modealignment and modemixing.
The number of IMFs
A statistical survey is also taken by investigating the EMG signals of muscle groups RF, BR, VM, and ST to sitting, standing, and walking exercises for all subjects. The averaged number of IMFs for each muscle is shown in Table 1. It has been clearly shown that MEMD and NAMEMD could guarantee the equal number of IMFs across EMG different channels. In addition, the number of IMFs via MEMD and NAMEMD have a larger amount compared to those of EEMD, indicating that more details of EMG frequency components can be obtains based on MEMD and NAMEMD results.
Modealignment
In order to statistically analyse the modealignment performance for multiplechannel EMGs, the correlation matrixes based on the motion segmentations of fourchannel EMG signals from all subjects in three exercise programs are calculated. The IMFs with the subfrequency energy less than 20Hz are removed as it contains much noise and has a low signaltonoise ratio. The mode alignment effects of decomposed IMFs of fourchannel EMG data obtained from the health group are identified in Table 2. Based on these results, twoway analysis of variance (ANOVA) is used to examine the influence of exercise programs (i.e., sitting, standing, and walking) and methods (i.e., EEMD, MEMD, and NAMEMD) on the performance index of modealignment (Table 3). The assessment results show that the methods have a significant main effect (\(p<0.01\)), and no interaction between exercise programs and methods (\(p>0.05\)). The statistic analysis with no interaction effect confirms that the three types of exercise programs equally represent the characteristic of functional activities of daily living. In order to further evaluate the difference among methods, the modealignment values in three exercise programs for each subject are averaged, and then the Oneway Repeated Measures ANOVA is used to compare the mode alignment of IMFs by EEMD, MEMD, and NAMEMD. It is clear that there is a significant difference among three methods (\(F=32.022\), \(p=0.000\)). By using the Least Significant Difference (LSD), the modealignment effect of NAMEMD is the best among three methods, and the effect of MEMD is merely better than that of EEMD (Fig. 5).
Modemixing
In this study, we also investigate the modemixing effect based on each muscle channel by using Eqs. (4) and (5). In order to avoid the effects of intersubject variability, the modemixing effects from all subjects are investigated. For each single subject, the decomposed IMFs for each muscle channel with a central frequency of the spectrum less than 20 Hz are also removed. The modealignment \(MM_{i,i+1}\) \((\text{i}=1, 2,\ldots,\text{I})\)from the remaining IMFs for each muscle channel are calculated. The modealignment effect for each muscle channel \(\tilde{M}\) is then obtained by averaging the set of \(MM_{i,i+1}\) \((\text{i}=1, 2,\ldots,\text{I}).\)Following this procedure, the modemixing effects of four EMG channels for three exercise programs are provided in Table 4.
In a similar way, the influence of exercise programs and methods on modemixing is first quantitatively analyzed through twoway ANOVA. Table 5 indicates the main effect of methods (\(p<0.01\)) as well as no interaction effect between two factors (\(p=0.706\)). The modemixing values in the three exercise programs of each subject are averaged, and the averaged values are applied to test the influence of methods on the performance of mode mixing by using Oneway Repeated Measures ANOVA and LSD. It can be seen from Fig. 5 that there are significant differences between two methods (EEMD vs. MEMD, EEMD vs. NAMEMD, and MEMD vs. NAMEMD) for the performance of mode mixing of decomposed IMFs. The NAMEMD achieves the best mode mixing performance compared to EEMD and MEMD, while MEMD far outperforms that of EEMD.
Discussion
The objective of this study is to evaluate a superior solution for the preprocessing of multichannel EMG signals as well as for the analysing of the IMF based frequency components related to multiple muscle groups. The muscle coordination often occurs in human motions, which is not only indicated by multichannel EMG signals, but also conducted by neuromuscular patterns [35]. Generally, the neuromuscular pattern is intrinsic for the specific exercise motions. Therefore, the singlechannelbased analyses for the observation of the nervous system and its corresponding muscle contraction are not sufficient.
Additionally, similar with the ECG lead system [36], it is also desirable to develop the EMG lead system in which the behaviors of motor units can be represented as a set of statistically independent sources.
The human exercise is often supported by multiple relative muscles. For example, the muscle groups of BF, VM, RF and ST are the muscles related to the knee movement such as standing, sitting, and walking. Hence, the use of the socalled fourlead system (the leads placed on muscles BF, VM, RF and ST) would well indicate the overall neuromuscular patterns, which are further controlled by the human brain activity. Moreover, it is a natural way to simultaneously decompose the multichannel EMG signals and analyse the subfrequency bands of multichannel EMG signals.
Although previous literatures have reported the successful applications of EMD/EEMD in the singlechannel EMGs [17], these approaches cannot solve the critical problem about the fusion and analysis of multichannel EMG signals [30, 34, 37]. Therefore, EEMD, MEMD and NAMEMD have been investigated in this study for the decomposition performance of four knee muscle groups associated with standing, sitting, and walking. Three criterions (the number of IMFs, modealignment and modemixing) are employed to quantitatively depict the decomposition efficiency.
It has been confirmed that both MEMD and NAMEMD (exclusive of EEMD) could provide an equal number of IMFs across EMG different channels. If the number of IMFs is unequal, then the decomposed subfrequency signals cannot be directly applied for the subsequent study. This also leads to the similar oscillation modes appearing in multiple IMFs (Fig. 3a).
The modealignment effect focuses on the crosschannel dependence. In order to compare the same indexed IMFs among muscle channels, a similar subfrequency band of the same indexed IMFs should also be observed. The statistics show that there is a significant difference among three methods (F = 32.022, p = 0.000). Moreover, the effect of NAMEMD is the best among three methods. In addition, the effect of MEMD is better than that of EEMD.
For the assessment of the modemixing effect, there are significant differences between two methods (EEMD vs. MEMD, EEMD vs. NAMEMD, and MEMD vs. NAMEMD). Specifically, NAMEMD achieves the best modemixing performance compared to EEMD and MEMD, and the effect of MEMD outperforms that of EEMD.
Limitation
The experimental data in this study was obtained from the Center for Machine Learning and Intelligent Systems, UCI. The data was donated by the Nueva Granada Military University and the Technopark node Manizales in Colombia. The physical characteristics of the participants were not recorded in the datasets. There also was no information about the prior nutritional intake, physical activity and environment conditions before all participants engaged in the experimental sessions. In addition, as the exercise programs (i.e., sitting, standing, and walking) are only taken from one measurement, the intrasubject variability such as random errors may not be avoided. The experiment description contained in the datasets did not clearly specify the location of electrodes placed on muscles BF, VM, RF, and ST.
Conclusions
This study proposed the noiseassisted multivariate empirical mode decomposition (NAMEMD) approach for the preprocessing of multiple channel EMG signals, by which the temporal and spatial characteristics across multiple muscle groups can be quantitatively depicted. The four muscle groups of BF, VM, RF, and ST associated with lower limb exercises (sitting, standing, and walking) of 11 healthy subjects were utilised for the assessment of the EMDbased approaches. A comparative study was provided by assessing the NAMEMD with Ensemble Empirical Mode Decomposition (EEMD), and Multivariate EMD (MEMD). Three criterions were used to assess the comparative outcomes, i.e., the number of intrinsic mode functions (IMFs), modealignment and modemixing. The results indicated that the current EMDbased approach of using EEMD was suboptimal for multichannel EMG signals due to its poor performance in relation to the three criterions. When compared with MEMD and NAMEMD, both approaches with data from lower limb EMG signals would guarantee an equal number of IMFs across channels. In addition, the statistical results showed that both the modealignment and modemixing effects of NAMEMD were superior to those of MEMD. This finding implied that NAMEMD is effective for simultaneously analysing IMFs based frequency bands. It has a vital clinical implication in terms of exploring the neuromuscular patterns that enable the coordination of multiple muscle groups for the purposes of performing daily activities.
Abbreviations
 BF:

biceps femoris
 EMG:

electromyography
 ECG:

electrocardiography
 EMD:

empirical mode decomposition
 EMG:

electromyography
 EEMD:

ensemble empirical mode decomposition
 GM:

goniometry
 IIR:

infinite impulse response
 IMF:

intrinsic mode functions
 MEMD:

multivariate empirical mode decomposition
 NAMEMD:

noiseassisted multivariate empirical mode decomposition
 PSD:

power spectral density
 RF:

rectus femoris
 ST:

semitendinosus
 STD:

standard deviation
 VM:

vastus medialis
 WGN:

white Gaussian noise
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Authors’ contributions
YZ found the utility of NAMEMD for the multichannel EMG signal processing, and interpreted this approach through a comparative study, provided a quantitative analysis for the decomposition performance evaluation, carried out the results and discussions, and drafted and revised the paper; PX and PYL verified the experimental data, statistic results, and revised the manuscript; KYD, QY, and TZ performed Matlab simulations; DZY supervised the project and checked the paper quality. All authors read and approved the final manuscript.
Acknowledgement
The authors are thankful for the supports from the School of Aeronautics and Astronautics (the University of Electronic Science and Technology of China, Chengdu, China), the Key Laboratory for NeuroInformation of Ministry of Education, School of Life Science and Technology (the University of Electronic Science and Technology of China, Chengdu, China), the Center for Information in BioMedicine (the University of Electronic Science and Technology of China, Chengdu, China), and Centre for Health Technologies (the University of Technology Sydney, Australia).
Competing interests
The authors declare that they have no competing interests.
Availability of data and materials
The datasets supporting the conclusions of this article are available in the repository UC Irvine Machine Learning Repository. http://archive.ics.uci.edu/ml/datasets/EMG+dataset+in+Lower+Limb.
Consent for publication
The manuscript has not been previously published, nor is it under consideration for publication elsewhere. All the authors have read and approved the manuscript. The authors will transfer copyright to the publisher upon acceptance of the manuscript.
Ethics approval and consent to participate
The experimental data were collected and recorded by the Nueva Granada Military University and the Technopark node Manizales in Colombia. The datasets were then donated to the Center for Machine Learning and Intelligent Systems, University of California Irvine (UCI) for research. UCI consented to cite these datasets in publications. This work was also approved by the Institution Research Ethics Board of University of Electronic Science and Technology of China (UESTC), and conducted according to the principles expressed in the Declaration of Helsinki.
Funding
This work is supported by the Fundamental Research Funds for the Central Universities, China (Grant No. ZYGX2015J118), the National Natural Science Foundation of China (Grant Nos. 51675087, 61522105), and the China Postdoctoral Science Foundation Funded Project (Grant No. 2017M612950).
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Yi Zhang, Peng Xu and Peiyang Li contributed equally to this work
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Zhang, Y., Xu, P., Li, P. et al. Noiseassisted multivariate empirical mode decomposition for multichannel EMG signals. BioMed Eng OnLine 16, 107 (2017). https://doi.org/10.1186/s1293801703979
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DOI: https://doi.org/10.1186/s1293801703979
Keywords
 EEMD
 MEMD
 NAMEMD
 Modealignment
 Modemixing
 Multichannel EMG signals