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An efficient method for analysis of EMG signals using improved empirical mode decomposition
Accepted Manuscript An Efficient Method for Analysis of EMG Signals using Improved Empirical Mode Decomposition Vipin K Mishra, Varun Bajaj, Anil Kumar, Dheeraj Sharma, G.K. Singh PII: DOI: Reference:
S1434-8411(16)31462-5 http://dx.doi.org/10.1016/j.aeue.2016.12.008 AEUE 51748
To appear in:
International Journal of Electronics and Communications
Received Date: Accepted Date:
6 October 2015 11 December 2016
Please cite this article as: V.K. Mishra, V. Bajaj, A. Kumar, D. Sharma, G.K. Singh, An Efficient Method for Analysis of EMG Signals using Improved Empirical Mode Decomposition, International Journal of Electronics and Communications (2016), doi: http://dx.doi.org/10.1016/j.aeue.2016.12.008
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An Efficient Method for Analysis of EMG Signals using Improved Empirical Mode Decomposition a
a
Vipin K Mishra, aVarun Bajaj, aAnil Kumar, aDheeraj Sharma and bG. K. Singh
Department of Electronics and Communication Engineering, PDPM Indian Institute of Information Technology, Design and Manufacturing Jabalpur, India b
Department of Electrical Engineering, Indian Institute Technology, Roorkee, India
Email:[email protected], [email protected], [email protected], [email protected], [email protected] Abstract In this paper, a simple technique with improved empirical mode decomposition (IEMD) in conjunction with four different features is used for the analysis of amyotrophic lateral sclerosis (ALS) and normal EMG signals. EMG signals consist of noise from various sources, such as electronic instruments, moving artifacts and electrical instruments. The empirical mode decomposition (EMD) method followed by median filter (MF) has been employed to remove the impulsive noise from intrinsic mode function (IMF) components generated through EMD. The filtered IMF components are summed together to generate a new signal. EMD process is further applied to new EMG signal to generate improved IMFs called as improved EMD method. In the IEMD algorithm for the first time, a new technique is proposed to choose the window size of median filter. For this, the features namely amplitude modulation bandwidth (BAM), frequency modulation bandwidth (BFM) , spectral moment of power spectral density (SMPSD), and first derivative of instantaneous frequency (MFDIF) extracted from the improved IMFs are used to discriminate between ALS and normal EMG signals. Finally, it is observed that IEMD method increases the discrimination ability of these features as compared to the EMD method and the adaptively fast ensemble empirical mode decomposition (AFEEMD) method. Keywords: Amyotrophic lateral sclerosis (ALS), electromyography (EMG), improved empirical mode decomposition (IEMD), impulsive noise, median filter. 1.
Introduction
Electromyography (EMG) is a technique used for diagnosis of neuromuscular diseases using electrical activities of the motor neurons (MN) and muscles. EMG technique converts these electrical signals into sound, graphs or numeric values [1]. EMG signal has been widely used by clinicians and researchers for the precise diagnosis of neuromuscular disorders. Neuromuscular disorders indicate the diseases related to MN, muscles, nerves and muscle tissues [2]. Other applications of EMG signal include engineering, medical science, sports
science, ergonomics and rehabilitation. In engineering, EMG signals are useful for human and machine interfacing, and robot control. In medical science, EMG signals are used for the identification of neuromuscular diseases [3]. The disorder in muscles creates a lot of diseases, especially the amyotrophic lateral sclerosis (ALS). ALS also known as Lou Gehrig’s disease is a fast progressing fatal disease caused by the motor neuron disorders [4]. ALS affects two motor neuron groups: lower motor neuron (LMN) and upper motor neuron (UMN), which are responsible for the voluntary movement of the body muscles. ALS progressively degenerates and makes the skeletal muscles weak. ALS damages the nervous control of the body by harming the nerve cells in spinal cord and brain [5-7]. The visual analysis of EMG signals is a challenging task because of nonstationary nature of EMG signals. Therefore, features extraction is useful for analysis of EMG signals.
Recently, various time and frequency domain features such as spectral peak level, zero crossing rate, mean frequency and the zero lag of autocorrelation function have been used for classification of ALS, myopathy and normal EMG signals [8]. To classify ALS, myopathy and normal EMG signals, features such as Lyapunov exponent, correlation dimension, correlation matrix, probability distribution function, and Hurst exponent have been used [9]. Analysis of the motor unit action potential (MUAP) and pattern of peak ratio interference have been used for the determination of subclinical bulbar involvement in ALS [10]. On the basis of systematic routine inspection of clinical data recorded from the sporadic amyotrophic lateral sclerosis (SALS) patients, a study has been done to find the prognostic values of biochemical markers in case of SALS [11]. Analysis of all genome expression profiles is performed for the discrimination of SALS from control signals [12]. Timefrequency based features are used for classification of ALS and normal EMG signals [13]. Discrete wavelet transform based features with k-nearest neighbourhood classifier have been employed for classification of ALS signals from normal EMG signals [14]. Mel frequency based Cepstral coefficient feature is applied on single MUAP instead of whole EMG signals to discriminate between ALS and normal EMG signals [15]. Some diagnostic marker such as kurtosis of histogram of EMG amplitude, kurtosis of crossing rate expansion of EMG signal, and clustering index are applied to linear discriminant analysis (LDA) classifier for classification of ALS and neurologically intact subjects [16]. The discrete wavelet transform based features have been used with random forest decision tree algorithm to classify ALS, myopathy and normal EMG signals [17]. Some statistical features obtained from discrete wavelet transform have been used with Fuzzy-SVM to classify ALS, myopathy and normal EMG signals [18]. Various features such as duration, area, number of phases, amplitude and rise time have been used for classification of myopathy, ALS and normal EMG signals [19]. The features such as
Cepstral coefficients, AR spectral measures, AR coefficients and time domain measures with fuzzy based classifier have been used to classify ALS, myopathy and normal EMG signals [20]. More recently, empirical mode decomposition (EMD) is a signal decomposition process widely used in biomedical signal processing, power signal processing, and seismic signals. Overlapping of different intrinsic mode function (IMF) components produced from EMD process of the signal is referred as mode mixing. Mode mixing is the problem arises in cases of EMD decomposition that results in failure of accurate decomposition of a signal. Some improved method such as mask signal improved EMD [21], adaptively fast ensemble empirical mode decomposition (AFEEMD) method [22], improved CEEMD (ICEEMD) [23] have been proposed to remove the problem of mode mixing. These methods are adequate to remove the noise in some conditions but are not effective in case of mode mixing caused by the impulse noise. The median filtering provides better results in case of impulse noise. EMG signals, which include noise of impulsive nature from various sources such as motion artifacts, electrical noise, instrumental noise and signal spurious background noise can be filtered suitably using the median filter (MF) [24]. Hence, in the improved empirical mode decomposition (IEMD) algorithm, selection of window size of median filter is proposed in order to overcome the effect of impulse noise. The features are extracted from analytic improved IMFs for analysis of ALS and normal EMG signals. Further, a comparative analysis is performed with the existing methods such as EMD and AFEEMD. The paper is organized as follows: Section 2 covers the dataset, description of EMD method, filter design with impulsive noise, and proposed steps of improved EMD. Section 3 provides analytic representation of improved IMFs. The features extracted from analytic improved IMFs are explained in Section 4. Finally, important findings and conclusions are summarized in Section 5 and Section 6 respectively. 2.
Methodology
2.1 Dataset Dataset consist of two classes; a normal class and an ALS patient class. Normal class consist of 4 females and 6 males of age between 21 to 37 years. No one from the normal class has any history of ALS or any other neuromuscular disorders. ALS patient class consists of 4 male and 4 female subjects of age between 35 to 67. Five patients from ALS class died within few years after the onset of the disease. Brachial biceps muscle was involved in this study, due to the frequent investigation of this muscle between two classes of subjects. For the recording of EMG signals following conditions were considered [25]; (i) low and constant level of contraction (ii) monitoring of signal through audio and visual feedback (iii) standard concentric needle electrode (iv) three
level of insertion on five places of muscles (v) the low and high pass filters were set at 10 kHz and 2 kHz respectively. Concentric electrode having 0.07 mm2 leading off area was used. The sampling rate of signal is 23437.5 Hz with the resolution of 16-bit. 2.2 Empirical mode decomposition: Empirical mode decomposition (EMD) is an adaptive algorithm for the decomposition of non-stationary signals. EMD decomposes EMG signals into some set of narrowband AM-FM components. Decomposed components have the intrinsic physical properties known as intrinsic mode function (IMF) [26]. Signal needs to satisfy two conditions for extraction of IMFs are as follows: (i) In the whole data set, the number of zero crossing and number of extrema should be equal or vary by at most one and (ii) At any instant, the mean value of envelope from maxima and minima should be zero [27]. Using these assumptions, any signal can be decomposed into number of IMFs through EMD process. The initial signal x t can be represented in form of IMFs and residual signal as: K
x t ck t rK t
(1)
k 1
Essentially, EMD decomposition process is a sifting process. The main aim of EMD is to decompose signal into narrow band signals that provide more inside information. 2.3 Filter design and impulse noise:
Impulse noise is a binary state sequence of nonstationary impulses having randomness in amplitude and position of occurrence. The nonstationary property of the impulse noise can be noticed by the observation of power spectrum of the noise [28]. Impulse noise is an acoustic noise of highly transient nature which may be present in digital images, communication signals, and biomedical signals. There is no universally accepted definition for impulse noise [29]. Many noise suppression methods are not suitable for the suppression of impulse noise due to the lack of second order moment [30]. The various sources of impulsive noise in EMG signals include baseline noise, electronic instruments, movement artifacts noise, noise due to power lines 50- 60 Hz, phone lines, Ethernet cables, and cable dishes etc. These noises are impulsive in nature as these affect the amplitude of signals for the small interval of time. The impulse n can be expressed as:
1 n 0 0 n 0
n
(2)
Here, n is the discrete time index. There are many models to represent the impulse noise such as BernoulliGaussian model, alpha stationary distribution, Poisson–Gaussian model, Binary-state model etc. [28]. The characteristic function for alpha stationary distribution can be represented as:
j t t t e
tan t 2 / log t
t,
1 j sgn t t ,
(3)
1 1
(4)
Here, is the median or mean value of alpha stationary distribution, is the characteristic exponent, is the symmetric parameter and is the coefficient of dispersion [31]. EMD signal decomposition method is dependent on mean of envelopes of the signals, which are affected by impulsive noise in case of EMG signals, as a result decomposition is not proper. Unity spectrum of impulse noise causes the presence of noise on all the IMF of an EMG signal [30]. For the suppression of impulsive noise, it is required to modify the time domain value of the signal. A median filter is a nonlinear and dynamic system used for smoothing of the voice signal and images. Some linear and dynamic system analysis method such as: impulse response, principle of superposition, frequency analysis, stability etc. cannot be used for the analysis of this filter [32]. Nonlinear median filter function can be represented as:
y n med x n k , x n k 1 ....x n ....x n k 1 , x n k
(5)
Where, x(n) is the input and y(n) is the output signal. Median filtering operation selects 2k+1 length samples of an input signal. Median process arranges those samples into magnitude sequence and chooses the magnitude value of middle sample. One dimension median filtering is being used here to remove the problem of mode mixing in EMD. If the size of window is 2k+1 or 2k with input sample as N size; for guaranteed filtering, the condition N≥2k or 2k+1 needs to be satisfied [33]. Assume that the amplitude sequencing x1 is the smallest and x2k+1 is the largest amplitude sample, then the output of median filtering for moving window along the data can be expressed as :
xk 1 med x1 , x2 ....xN xk xk 1 2
N 2k 1 N 2k
(6)
The median filter in expression (6) is a sliding or moving window filter. The median filter of small window size eliminates the noise effectively at the cost of some amount of information loss, whereas the large window size median filter preserve the information at the cost of reduced impulse noise suppression ability [32]. 2.4 Improved EMD:
EMD decomposes signal into some set of different frequencies components known as IMFs. Different frequencies of IMF components enable to use variable window median filtering. The median filtering of higher frequency IMF component is smaller window size and the size of window increases with the decrease in frequency of IMF (or increase in the number of IMF), which successfully removes the impulse noise without major loss of important data. The process of choosing a window size based on the frequency of IMF components is named as variable window median filtering. The process EMD is improved by using below steps: Step 1: Assume an original signal is x t and apply EMD algorithm on this signal to get IMF components ck t and residue, where k 1, 2, .....K and K is the total number of IMF components. Residue is basically a monotonic or constant function. Step 2: Window size of median filtering for first four IMF components 2 k 1 *3 and the rest of IMFs the size 2 k 2 are applied to get filtered IMFs d k (t ) ; here, k is the number of IMF components.
Step 3: Sum of all the filtered IMF components d k (t ) to get filtered signal y (t ) .
Step 4: Apply EMD algorithm on y (t ) to get improved IMFs em (t ) ; here, m 1, 2,......, M and M is the total number of improved IMFs. Further, the processing can be done on these improved IMFs. The filtering process is applied to IMF components rather than signal. The size of filter window rises with the order of IMF component. This overcomes the problem of window size selection for particular IMF. These all steps are shown in Fig. 1. 3.
Analytic representation of improved IMFs IMF components are real signals, which are converted into an analytic form using Hilbert transform.
Analytic signals are suitable to find out instantaneous frequency and instantaneous amplitude of the signals. The analytic signal of mth IMF is defined as:
zm t em t jem t Am t e jm t
(7)
Where, Am t and m t are called instantaneous amplitude and the instantaneous phase angle, which can be defined as:
Am t
e t e t 2 m
2 m
and
em t em t
m t arctan
(8)
The instantaneous frequency of the signal is expressed as the rate of change of m t with respect to time
fm t
1 dm t 2 dt
(9)
The instantaneous frequency is the single-valued function of time [26].
EMG signal x(t)
IMF extracted after applying EMD c1(t)
c2(t)
MF
MF
d1(t)
d2(t)
……………
cK(t) MF
……………
dK(t)
Reconstructed filtered signal y(t)
Improved IMF extracted after applying EMD
e1(t)
e2(t)
…………….
eM(t)
Fig. 1. Block diagram of improved EMD 4.
Features extracted from improved IMFs
4.1 Bandwidth computation from analytic improved IMFs
The bandwidth of any signal provides information about the spread of frequency along the signal length. Signals may have the bandwidth due to amplitude modulation and due to large deviation in the instantaneous frequencies. These two bandwidth for analytic signal z t can be defined as:
2 2 d t 2 1 dA t B A t dt dt E dt dt 2
(10)
Here, E is the energy of analytic improved IMF and can be represented as [34]:
1 d t 2 A t dt E dt
(11)
From expression (10), it is clear that the bandwidth of analytic signal depends upon two components, first component is the amplitude and second component is the phase of the signal. From the above expression, bandwidth due to the amplitude modulation (BAM) and bandwidth due to the frequency modulation (BFM) can be represented as: 1 dA t dt E dt 2
BAM
(12)
1 d t A2 t dt E dt 2
BFM
(13)
4.2 Spectral moments of power spectral density (SMPSD) from analytic improved IMFs Power spectral density (PSD) is defined as the frequency response of any signal. It gives information about the distribution of average power in terms of frequency. PSD is suitable to find out power and dominant frequency of the signal. PSD of analytic signal z(t) can be defined as:
1 sz f lim T 2T
T
z t e
T
dt 2
j 2 ft
(14)
The first order spectral moment of PSD (SMPSD) provides information of higher order shape of the signal [35]. It can be represented as:
N
SM PSD k PSDk k 1
(15)
4.3 Mean of first derivative of instantaneous frequency (MFDIF) computation from analytic improved IMFs:
This feature is the first derivative of instantaneous frequency (MFDIF) that provides information about the difference between adjacent instantaneous frequencies of the signal. The mean of f can be represented as [36]:
N 1
MFDIF l 1
f (l ) N 1
where
f diff fi
(16)
Here, N is the number of samples of instantaneous frequency.
The least squares support vector machine (LS-SVM) classifier has been used for classification of ALS and normal EMG signals. The detailed description of LS-SVM classifier is available in [37-38]. 5.
Results and Discussion The presence of noise in EMG signal from various sources creates the changes in physical characteristics of
the signal. The noise in signal modifies the amplitude of signal for short duration and may present in entire range of frequency, due to which these noises can be considered as impulsive noise. Fig. 2 shows EMG signal with IMF components c1(t)-c8(t) and the residue rK(t) produced by EMD, before the median filtering. Due to the presence of impulse noise in EMG signal, mode mixing is present in IMF components, and the reasonable IMF components cannot be found through EMD. In the proposed method, EMD followed by the median filter is used to remove the impulse noise from IMF components, which are ultimately summed to generate the new filtered EMG signal. The filtered EMG signal is decomposed into improved IMF components through EMD process. Fig. 3 shows the filtered EMG signal and improved IMF components e1(t)-e8(t) with residue eM(t) induced by IEMD process. IMF components are arranged in decreasing order of the frequency and increasing order of IMF components. The median filtering is a robust way to eliminate the impulse noise from any signal. It is difficult to eliminate the noise completely, due to which the mode mixing may present in improved IMF components to some proportion. Median filtering of IMF components reduces the noise from EMG signals and improves the discrimination performance of the features. The discrimination results in Table 1-4 shows the effectiveness of median filtering in case of impulse noise in EMG signal. Table 1 shows the comparison of discrimination abilities of BAM feature in case of EMD, AFEEMD and proposed IEMD methods. It is clear from the Table 1 that the probability value is higher in case of EMD and AFEEMD methods as compared to IEMD method, which means that discrimination ability of BAM feature
extracted from IEMD method is better than EMD and AFEEMD methods. It is observed that the feature BAM of first four IMFs are statistically significant, which shows that first four IMF components have better discrimination ability. The feature BAM of IMFs for normal EMG signals is larger as compared to ALS EMG signals, it may be due to the rate of change of amplitude envelopes of IMFs is higher in normal EMG signals. Fig. 4 shows the discrimination performance of first four IMF components of feature BAM. Fig.4 (a) shows Kruskal-Wallis plot for EMD method and Fig. 4 (b) depicts Kruskal-Wallis plot for IEMD method. It is clear from visual inspection of plots that IEMD method is statistically significant for analysis of ALS and normal EMG signals. Table 2 depicts the discrimination performance of feature BFM in case of EMD, AFEEMD and improved EMD methods. From the table, it is clear that the probability value of feature BFM in case of proposed IEMD method is lower as compared to EMD and AFEEMD methods, which shows that feature BFM of IEMD method has better discrimination capability. Discrimination ability of first four IMFs is significantly better as compared to other IMFs. BFM
Fig. 5 shows Kruskal-Wallis plot of feature BFM
to describe the discrimination between ALS and normal of EMG signals. Fig. 5(a) shows the discrimination ability of feature BFM by using EMD method and Fig. 5(b) illustrates the discrimination ability of feature BFM by using IEMD method. Table 3 describes the discrimination ability of feature SMPSD in case of EMD, AFEEMD and IEMD methods. The value of probability is lower in case of IEMD method compared to EMD and AFEEMD methods, which shows the better discrimination performance of IEMD method. For the first four IMFs discrimination ability is significantly greater than other IMFs. The feature SMPSD of IMFs of ALS EMG signals is greater as compared to normal EMG signals. Fig. 6 shows the performance of EMD, and IEMD in case of SMPSD feature. Fig. 6(a) shows the performance of SMPSD feature using EMD method and Fig. 6(b) presents the performance of SMPSD feature using IEMD method. Table 4 exhibits the discrimination performance of feature MFDIF in case of typical EMD, AFEEMD and IEMD methods. From the probability values of the table, it is clear that the performance of proposed IEMD method is better than EMD and AFEEMD methods. Discrimination capability of first four IMFs component of IEMD method is higher as
to other IMFs. The feature MFDIF of IMFs for ALS EMG signals is larger
as compared to normal EMG signals. Fig. 7 shows the discrimination performance of MFDIF feature in case of
EMD, and proposed IEMD methods. Fig. 7(a) depicts the performance of MFDIF feature using EMD method and Fig. 7(b) shows the performance of MFDIF feature using proposed IEMD method. The probability value of the Table 1-4 clearly shows that the first four IMFs of all the features are statically significant as compared to all other IMF components. The features namely amplitude modulation bandwidth (BAM) and frequency modulation bandwidth (BFM) with spectral moments of power spectral density (SMPSD) and first derivative of instantaneous frequency (MFDIF) are used as an input features to the LS-SVM classifier with the redial basis function kernel. Table 5 shows the classification accuracy (%) of ALS and normal EMG signals classification using EMD, AFEEMD, and IEMD methods for first four IMFs. It can be seen from Table 5 that IEMD based features provided better classification accuracy of ALS and normal EMG signals as compare to EMD and AFEEMD. Hence the result presented in this paper shows the capability of proposed IEMD based features for diagnosis of ALS using EMG signals. 6.
Conclusion In this paper, we have demonstrated a new median filtering based improved EMD method for the
discrimination of ALS and normal EMG signals. The direct use of EMD cannot decompose the noisy signals efficiently due to the effect of impulse noise in the amplitude of the signals. The median filtering is a valuable tool to remove impulse noise from EMG signals. Therefore, the proposed method is capable of suppressing the impulse noise from EMG signals without losing any useful information. Thus, the use of median filter of different window size for each IMF components improves the filtering performance. The proposed IEMD method is strong enough for accurate decomposition of EMG signals containing impulse noise. The discrimination results after the processing of ALS and normal EMG signals demonstrate effectiveness of the proposed method. Four features BAM, BFM, SMPSD and MFDIF have been employed for the analysis of ALS and normal EMG signals. These parameters provide significant differences between ALS and normal EMG signals. The discrimination capability of the features is improved in IEMD method as compared to EMD and AFEEMD methods. Apart from these, the classification performance of proposed IEMD method is better as compare to exiting EMD and AFEEMD methods for diagnosis of ALS using EMG signals. The proposed method can be applied for the analysis of other non-stationary signals possessing the impulse noise.
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Fig. 2. Empirical mode decomposition of initial EMG signal x t
Fig. 3. Empirical mode decomposition of improved EMG signal y t
Table 1. Value of probability and mean ± std. of eight IMF components of BAM feature for EMD, AFEEMD and IEMD methods.
Methods
EMD
AFEEMD
IMF No.
Signal type
Mean ± std.
Probability
Mean ± std.
IMF1
ALS
0.057±0.0077
4.26×10-7
0.333±0.0866
IMF2
Normal ALS
6.72×10-7
0.3148±0.0789 0.1081±0.0392
IMF3
Normal ALS
0.0144±0.0073 0.0114±0.0106
Normal
0.0112±0.0069
ALS
0.0103±0.0095
IMF4
Normal ALS
IMF5
0.0102±0.009 0.0091±0.0067
ALS
0.0086±0.0069
Normal ALS
0.0087±0.0074 0.0101±0.0079
Normal
0.0084±0.0073
ALS
0.009±0.0077
Normal
0.0109±0.0073
IMF8
3.70×10
-4
2.14 ×10
-3
0.0106±0.0081
Normal IMF6
IMF7
0.0189±0.0077 0.012±0.0075
Probability 1.8×10-4
1.37×10
2.08×10
0.0437±0.0106
1.06×10-05
0.0188±0.0068
5.05×10
1.44×10
-1
3.87×10
-08
0.0123±0.007
0.1382±0.0532
6.05×10-8
0.174±0.0488 0.0535±0.0162
2.1×10-12
0.0676±0.0159 0.0262±0.0084
2.4×10-19
0.0351±0.0087 7.37×10-9
0.0224±0.0074 4.022×10-3
0.0139±0.0081 5.53×10
-02
0.0104±0.008
0.0156±0.0067 0.0124±0.0088
7.68×10
0.0095±0.0068 0.009±0.0068
4.96×10-1
-1
1.82×10-1
0.008±0.0066 9.28×10-1
Probability
0.0181±0.0082
0.0133±0.0058 -1
Mean ± std.
-1
0.1099±0.0326 0.0387±0.0129
0.0209±0.0058 -2
I-EMD
0.0117±0.0057 0.0084±0.0057
7.04×10-4
0.0103±0.0065
0.0086±0.0063
0.007±0.0049 8.76×10-1
0.009±0.0074
3.96×10-3
0.0088±0.0062
Table 2. Value of probability and mean ± std. of eight IMF components of BFM
feature for EMD,
AFEEMD and IEMD methods.
Methods IMF No. Signal type IMF1
IMF2
IMF3
IMF4
IMF5
IMF6
IMF7
IMF8
EMD Mean ± std.
Probability
3
ALS
1.33×10 ±358.36
Normal
8
5.65×10-6
1.52×10 ±349.71
ALS
646.87±213.77
Normal
705.85±175.85
ALS
AFEEMD
421.35±204.83
Normal
438.57±125.50
ALS
285.83±151.95
Normal
305.55±96.56
ALS
226.08±121.92
Normal
215.66±92.13
ALS
167.54±95.31
Normal
158.77±85.01
ALS
136.49±76.29
Normal
118.61±69.42
ALS
103.39±62.45
Normal
120.03±62.21
3.96×10-3
Mean ± std. 1.40×10
+04
1.42×10
+04
7.65×10
+02
I-EMD Probability
±2.96×10
+03
±3.32×10
+03
±1.72×10
+03
6.86×10
-01
1.359×10-3 1.81×10
-2
1.32×10 1.62×10
+03
±386.1291
4.22×10
5.54×10-09
2.18×10
322.8955±110.3514
7.6×10
7.52×10-1 1.25×10-1
3
3.25×103±1.25×103 1.68×103±671.32
4.75×10
1.14×103±477.53
2.6×10-11 1.6×10-11 5.20×10-6
3
1.47×10 ±588.44 7.73×10
-02
845.04±413.91
1.67×10-03
3
1.04×10 ±530.25
203.2098±82.8865 2.81×10-02 362.5539 81.9353 208.235±69.4117
566.59±268.02
150.5367±72.734 6.66×10-01 141.7612 62.9095 141.7612±62.9095 362.5539 81.9353
390.65±191.07
116.4382±61.2378
272.87±137.84
122.665±74.7709
3.69×10-7
2.28×10 ±741.38 -05
362.5539±81.9353 -1
4
8.99×10 ±3.36×10
3
667.1958±155.2054 -1
3
4.21×103±1.22×103
±478.6641
586.5573± 185.2538
Probability
3
1.11×10 ±3.07×10 -01
9.24×10+02±1.64×10+03 +03
Mean ± std.
9.96×10-01
1.72×10-02
691.58±369.1 2.24×10-02
487.99±280.36
329.65±216.58
3.96×10-03
Table 3. Value of probability and mean ± std. of eight IMF components of SMPSD feature for for EMD, AFEEMD and IEMD methods.
Methods IMF No. Signal type IMF1
ALS Normal
IMF2
ALS Normal
IMF3
ALS Normal
IMF4
IMF5
IMF6
IMF7
IMF8
ALS
EMD Mean ± std.
AFEEMD Probability
8
9
8
8
8
9
8
8
8
8
6.71×10 ±1.88×10
8.73×10-7
1.14×10 ±4.38×10 5.99×10 ±1.24×10
1.15×10-5
2.81×10 ±8.19×10 2.22×10 ±4.78×10
4 ×10
-04
1.43×108±2.98×108 8
8
4.24×10 ±8.88×10 8
2.08×10 ±4.71×10
ALS
3.71×108±6.23×108 8
3.18×10-5
2.42×10 ±4.84×10
ALS
8.18×108±2.08×109 8
1.42×10
+06
8.36×10
+06
5.72×10
+06
6.94×10
+07
2.66×10 8.68×10
1.32×10
-02
8
Normal
2.52×10
+06
Probability
±1.13×10
+07
±7.16×10
+06
±1.78×10
+07
±2.49×10
+07
±1.54×10
+08
2.17×10+07±4.48×10+07
8
Normal
Mean ± std.
3.49×10
9
+07
+4.36×10 ±2.24×10
+07
±1.18×10
+08
Normal
5.6×10 ±2.81×10
8.62×10
ALS
2.53×109±8.27×109
2.69×10+08±9.90×10+08
Normal
5.68×109±5.69×1010
ALS
5.06×1011±4.65×1012
Normal
9
3.89×10-06
±1.38×10
+08
7.54×10+07±1.67×10+08 2×10-03
10
9.07×10 ±6.42×10
1.15×10
±2.08×10
+08
6
6
6
2.61×10 ±1.42×10
1.88×10
1.02×10
-02
2.3×10-10
3.19×106±7.51×106 7
8.52×10-7
7
1.05×10 ±2.56×10 7
2.85×10-03
7
1.59×10 ±3.59×10
9.87×107±1.6×108 -02
6.14×10-6
7
8.37×107±3.6×108 2.22×10-02
9.69×10-5
1.25×10 ±8.91×10
3.68×107±7.42×107 6.10×10-05
7
3.49×10-5
8
4.87×10 ±1.52×10
1.98×108±4.96×108
2.22×10-04
7.66×107±1.42×108
3.50×10+08±8.53×10+08 +08
7
6.32×107±2.91×108 7.18×10-07
1.45×10+08±2.06×10+08 +07
Probability
6
1.09×107±4.53×107 1.75×10-05
+08 +08
Mean ± std. 9.25×10 ±6.87×10
4.74×10-03
1.65×10+08±2.16×10+08 7.57×10
-6
+08
I-EMD
2.73×108±5.15×108 1.60×10-01
3.96×10-03
1.4×108±2.59×108
Table 4. Value of probability and mean ± std. of eight IMF components of MFDIF feature for for EMD, AFEEMD and IEMD methods. Methods IMF No. Signal type IMF1
IMF2
IMF3
IMF4
IMF5
IMF6
IMF7
IMF8
ALS
EMD Mean ± std. 812.09±328.52
Normal
806.59±274.54
ALS
390.65±164.12
Normal
346.59±135.83
ALS
176.43±105.58
Normal
130.33±77.89
ALS
86.95±68.08
Normal
59.79±41.44
ALS
48.01±38.27
Normal
33.05±20.89
ALS
30.54±19.54
Normal
23.51±14.61
ALS
206.99±258.38
Normal
136.4±142.38
ALS
96.25±83.36
Normal
83.5±89.09
AFEEMD Probability 4.77×10
-01
Mean ± std. 1.19×10
+04
I-EMD Probability
±3.16×10
+02
1.28×10
-1
+04
2.74×10
5.20×10
-6
+03
5.2×10 ± 5.90×10 7.79×10
+02
2.17×10
+03
+02
±6.07×10
+02
±3.26×10
+02
1.00×10-4
8.60×10
-3
7.00×10 5.32×10
+02
9.60×10
1.09×10
±5.84×10
+01
±2.04×10
+01
±1.40×10
1.95×10
+01
5.26×10
±1.20×10
4.96×103±1.3×103
1.77×10-6
2.34×103±646.95
1.5×10-13
1.76×103±479.73 3.84×10-1
999.86±341.09
3.34×10-8
773.24±294.42 3.98×10
-2
446.87±245.55
2.64×10
-2
231.21±136.49
5.84×10
-1
1.15×10-5
347.25±170.5 8.73×10-6
177.11±129.14
+01
+01
6.67×10-6
4.2×10 ±955.2 -3
+01
2.09×10+01±1.28×10+01
1.01×10 ±1.06×10
3
+01
3.14×10+01±2.14×10+01 2.17×10
4.08×10-01
+02
6.06×10+01±3.83×10+01 3.90×10
6.64×10-05
±1.32×10
+02
1.87×10+02±7.55×10+01 1.27×10
-3
±1.52×10
+02
Probability 3
9.61×10 ±726.84 -2
1.87×10+03±3.18×10+02 +02
4
3
1.1503×10 ± 485.7054 -2
Mean ± std.
103.62±83.01
2.50×10-02
84.93±68.07 2.17×10-01
57.63±52.17 50.03±43.97
3.96×10-03
Table 5 Classification accuracy (%) of ALS and Normal EMG signals classification using for EMD, AFEEMD and IEMD methods. Kernel IMFs
EMD
AFEEMD
IEMD
(Parameters) IMF1 RBF (
1)
IMF2 IMF3 IMF4
89.91 92.66 91.74 88.99
90.47 91.74 90.47 85.71
92.66 96.33 94.49 90.47
Fig. 4. Comparison of BAM parameter for the four different IMF components of ALS and normal EMG signals (a) using typical EMD method, (b) using I-EMD method, and (c) using AFEEMD method.
Fig. 5. Comparison of BFM parameter for the four different IMF components of ALS and normal EMG signals (a) using typical EMD method, (b) using I-EMD method, and (c) using AFEEMD method.
Fig. 6. Comparison of SMPSD parameter for the four different IMF components of ALS and normal EMG signals (a) using typical EMD method, (b) using I-EMD method, and (c) using AFEEMD method.
Fig. 7. Comparison of MFDIF parameter for the four different IMF components of ALS and normal EMG signals (a) using typical EMD method, (b) using I-EMD method, and (c) using AFEEMD method.
S1434-8411(16)31462-5 http://dx.doi.org/10.1016/j.aeue.2016.12.008 AEUE 51748
To appear in:
International Journal of Electronics and Communications
Received Date: Accepted Date:
6 October 2015 11 December 2016
Please cite this article as: V.K. Mishra, V. Bajaj, A. Kumar, D. Sharma, G.K. Singh, An Efficient Method for Analysis of EMG Signals using Improved Empirical Mode Decomposition, International Journal of Electronics and Communications (2016), doi: http://dx.doi.org/10.1016/j.aeue.2016.12.008
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
An Efficient Method for Analysis of EMG Signals using Improved Empirical Mode Decomposition a
a
Vipin K Mishra, aVarun Bajaj, aAnil Kumar, aDheeraj Sharma and bG. K. Singh
Department of Electronics and Communication Engineering, PDPM Indian Institute of Information Technology, Design and Manufacturing Jabalpur, India b
Department of Electrical Engineering, Indian Institute Technology, Roorkee, India
Email:[email protected], [email protected], [email protected], [email protected], [email protected] Abstract In this paper, a simple technique with improved empirical mode decomposition (IEMD) in conjunction with four different features is used for the analysis of amyotrophic lateral sclerosis (ALS) and normal EMG signals. EMG signals consist of noise from various sources, such as electronic instruments, moving artifacts and electrical instruments. The empirical mode decomposition (EMD) method followed by median filter (MF) has been employed to remove the impulsive noise from intrinsic mode function (IMF) components generated through EMD. The filtered IMF components are summed together to generate a new signal. EMD process is further applied to new EMG signal to generate improved IMFs called as improved EMD method. In the IEMD algorithm for the first time, a new technique is proposed to choose the window size of median filter. For this, the features namely amplitude modulation bandwidth (BAM), frequency modulation bandwidth (BFM) , spectral moment of power spectral density (SMPSD), and first derivative of instantaneous frequency (MFDIF) extracted from the improved IMFs are used to discriminate between ALS and normal EMG signals. Finally, it is observed that IEMD method increases the discrimination ability of these features as compared to the EMD method and the adaptively fast ensemble empirical mode decomposition (AFEEMD) method. Keywords: Amyotrophic lateral sclerosis (ALS), electromyography (EMG), improved empirical mode decomposition (IEMD), impulsive noise, median filter. 1.
Introduction
Electromyography (EMG) is a technique used for diagnosis of neuromuscular diseases using electrical activities of the motor neurons (MN) and muscles. EMG technique converts these electrical signals into sound, graphs or numeric values [1]. EMG signal has been widely used by clinicians and researchers for the precise diagnosis of neuromuscular disorders. Neuromuscular disorders indicate the diseases related to MN, muscles, nerves and muscle tissues [2]. Other applications of EMG signal include engineering, medical science, sports
science, ergonomics and rehabilitation. In engineering, EMG signals are useful for human and machine interfacing, and robot control. In medical science, EMG signals are used for the identification of neuromuscular diseases [3]. The disorder in muscles creates a lot of diseases, especially the amyotrophic lateral sclerosis (ALS). ALS also known as Lou Gehrig’s disease is a fast progressing fatal disease caused by the motor neuron disorders [4]. ALS affects two motor neuron groups: lower motor neuron (LMN) and upper motor neuron (UMN), which are responsible for the voluntary movement of the body muscles. ALS progressively degenerates and makes the skeletal muscles weak. ALS damages the nervous control of the body by harming the nerve cells in spinal cord and brain [5-7]. The visual analysis of EMG signals is a challenging task because of nonstationary nature of EMG signals. Therefore, features extraction is useful for analysis of EMG signals.
Recently, various time and frequency domain features such as spectral peak level, zero crossing rate, mean frequency and the zero lag of autocorrelation function have been used for classification of ALS, myopathy and normal EMG signals [8]. To classify ALS, myopathy and normal EMG signals, features such as Lyapunov exponent, correlation dimension, correlation matrix, probability distribution function, and Hurst exponent have been used [9]. Analysis of the motor unit action potential (MUAP) and pattern of peak ratio interference have been used for the determination of subclinical bulbar involvement in ALS [10]. On the basis of systematic routine inspection of clinical data recorded from the sporadic amyotrophic lateral sclerosis (SALS) patients, a study has been done to find the prognostic values of biochemical markers in case of SALS [11]. Analysis of all genome expression profiles is performed for the discrimination of SALS from control signals [12]. Timefrequency based features are used for classification of ALS and normal EMG signals [13]. Discrete wavelet transform based features with k-nearest neighbourhood classifier have been employed for classification of ALS signals from normal EMG signals [14]. Mel frequency based Cepstral coefficient feature is applied on single MUAP instead of whole EMG signals to discriminate between ALS and normal EMG signals [15]. Some diagnostic marker such as kurtosis of histogram of EMG amplitude, kurtosis of crossing rate expansion of EMG signal, and clustering index are applied to linear discriminant analysis (LDA) classifier for classification of ALS and neurologically intact subjects [16]. The discrete wavelet transform based features have been used with random forest decision tree algorithm to classify ALS, myopathy and normal EMG signals [17]. Some statistical features obtained from discrete wavelet transform have been used with Fuzzy-SVM to classify ALS, myopathy and normal EMG signals [18]. Various features such as duration, area, number of phases, amplitude and rise time have been used for classification of myopathy, ALS and normal EMG signals [19]. The features such as
Cepstral coefficients, AR spectral measures, AR coefficients and time domain measures with fuzzy based classifier have been used to classify ALS, myopathy and normal EMG signals [20]. More recently, empirical mode decomposition (EMD) is a signal decomposition process widely used in biomedical signal processing, power signal processing, and seismic signals. Overlapping of different intrinsic mode function (IMF) components produced from EMD process of the signal is referred as mode mixing. Mode mixing is the problem arises in cases of EMD decomposition that results in failure of accurate decomposition of a signal. Some improved method such as mask signal improved EMD [21], adaptively fast ensemble empirical mode decomposition (AFEEMD) method [22], improved CEEMD (ICEEMD) [23] have been proposed to remove the problem of mode mixing. These methods are adequate to remove the noise in some conditions but are not effective in case of mode mixing caused by the impulse noise. The median filtering provides better results in case of impulse noise. EMG signals, which include noise of impulsive nature from various sources such as motion artifacts, electrical noise, instrumental noise and signal spurious background noise can be filtered suitably using the median filter (MF) [24]. Hence, in the improved empirical mode decomposition (IEMD) algorithm, selection of window size of median filter is proposed in order to overcome the effect of impulse noise. The features are extracted from analytic improved IMFs for analysis of ALS and normal EMG signals. Further, a comparative analysis is performed with the existing methods such as EMD and AFEEMD. The paper is organized as follows: Section 2 covers the dataset, description of EMD method, filter design with impulsive noise, and proposed steps of improved EMD. Section 3 provides analytic representation of improved IMFs. The features extracted from analytic improved IMFs are explained in Section 4. Finally, important findings and conclusions are summarized in Section 5 and Section 6 respectively. 2.
Methodology
2.1 Dataset Dataset consist of two classes; a normal class and an ALS patient class. Normal class consist of 4 females and 6 males of age between 21 to 37 years. No one from the normal class has any history of ALS or any other neuromuscular disorders. ALS patient class consists of 4 male and 4 female subjects of age between 35 to 67. Five patients from ALS class died within few years after the onset of the disease. Brachial biceps muscle was involved in this study, due to the frequent investigation of this muscle between two classes of subjects. For the recording of EMG signals following conditions were considered [25]; (i) low and constant level of contraction (ii) monitoring of signal through audio and visual feedback (iii) standard concentric needle electrode (iv) three
level of insertion on five places of muscles (v) the low and high pass filters were set at 10 kHz and 2 kHz respectively. Concentric electrode having 0.07 mm2 leading off area was used. The sampling rate of signal is 23437.5 Hz with the resolution of 16-bit. 2.2 Empirical mode decomposition: Empirical mode decomposition (EMD) is an adaptive algorithm for the decomposition of non-stationary signals. EMD decomposes EMG signals into some set of narrowband AM-FM components. Decomposed components have the intrinsic physical properties known as intrinsic mode function (IMF) [26]. Signal needs to satisfy two conditions for extraction of IMFs are as follows: (i) In the whole data set, the number of zero crossing and number of extrema should be equal or vary by at most one and (ii) At any instant, the mean value of envelope from maxima and minima should be zero [27]. Using these assumptions, any signal can be decomposed into number of IMFs through EMD process. The initial signal x t can be represented in form of IMFs and residual signal as: K
x t ck t rK t
(1)
k 1
Essentially, EMD decomposition process is a sifting process. The main aim of EMD is to decompose signal into narrow band signals that provide more inside information. 2.3 Filter design and impulse noise:
Impulse noise is a binary state sequence of nonstationary impulses having randomness in amplitude and position of occurrence. The nonstationary property of the impulse noise can be noticed by the observation of power spectrum of the noise [28]. Impulse noise is an acoustic noise of highly transient nature which may be present in digital images, communication signals, and biomedical signals. There is no universally accepted definition for impulse noise [29]. Many noise suppression methods are not suitable for the suppression of impulse noise due to the lack of second order moment [30]. The various sources of impulsive noise in EMG signals include baseline noise, electronic instruments, movement artifacts noise, noise due to power lines 50- 60 Hz, phone lines, Ethernet cables, and cable dishes etc. These noises are impulsive in nature as these affect the amplitude of signals for the small interval of time. The impulse n can be expressed as:
1 n 0 0 n 0
n
(2)
Here, n is the discrete time index. There are many models to represent the impulse noise such as BernoulliGaussian model, alpha stationary distribution, Poisson–Gaussian model, Binary-state model etc. [28]. The characteristic function for alpha stationary distribution can be represented as:
j t t t e
tan t 2 / log t
t,
1 j sgn t t ,
(3)
1 1
(4)
Here, is the median or mean value of alpha stationary distribution, is the characteristic exponent, is the symmetric parameter and is the coefficient of dispersion [31]. EMD signal decomposition method is dependent on mean of envelopes of the signals, which are affected by impulsive noise in case of EMG signals, as a result decomposition is not proper. Unity spectrum of impulse noise causes the presence of noise on all the IMF of an EMG signal [30]. For the suppression of impulsive noise, it is required to modify the time domain value of the signal. A median filter is a nonlinear and dynamic system used for smoothing of the voice signal and images. Some linear and dynamic system analysis method such as: impulse response, principle of superposition, frequency analysis, stability etc. cannot be used for the analysis of this filter [32]. Nonlinear median filter function can be represented as:
y n med x n k , x n k 1 ....x n ....x n k 1 , x n k
(5)
Where, x(n) is the input and y(n) is the output signal. Median filtering operation selects 2k+1 length samples of an input signal. Median process arranges those samples into magnitude sequence and chooses the magnitude value of middle sample. One dimension median filtering is being used here to remove the problem of mode mixing in EMD. If the size of window is 2k+1 or 2k with input sample as N size; for guaranteed filtering, the condition N≥2k or 2k+1 needs to be satisfied [33]. Assume that the amplitude sequencing x1 is the smallest and x2k+1 is the largest amplitude sample, then the output of median filtering for moving window along the data can be expressed as :
xk 1 med x1 , x2 ....xN xk xk 1 2
N 2k 1 N 2k
(6)
The median filter in expression (6) is a sliding or moving window filter. The median filter of small window size eliminates the noise effectively at the cost of some amount of information loss, whereas the large window size median filter preserve the information at the cost of reduced impulse noise suppression ability [32]. 2.4 Improved EMD:
EMD decomposes signal into some set of different frequencies components known as IMFs. Different frequencies of IMF components enable to use variable window median filtering. The median filtering of higher frequency IMF component is smaller window size and the size of window increases with the decrease in frequency of IMF (or increase in the number of IMF), which successfully removes the impulse noise without major loss of important data. The process of choosing a window size based on the frequency of IMF components is named as variable window median filtering. The process EMD is improved by using below steps: Step 1: Assume an original signal is x t and apply EMD algorithm on this signal to get IMF components ck t and residue, where k 1, 2, .....K and K is the total number of IMF components. Residue is basically a monotonic or constant function. Step 2: Window size of median filtering for first four IMF components 2 k 1 *3 and the rest of IMFs the size 2 k 2 are applied to get filtered IMFs d k (t ) ; here, k is the number of IMF components.
Step 3: Sum of all the filtered IMF components d k (t ) to get filtered signal y (t ) .
Step 4: Apply EMD algorithm on y (t ) to get improved IMFs em (t ) ; here, m 1, 2,......, M and M is the total number of improved IMFs. Further, the processing can be done on these improved IMFs. The filtering process is applied to IMF components rather than signal. The size of filter window rises with the order of IMF component. This overcomes the problem of window size selection for particular IMF. These all steps are shown in Fig. 1. 3.
Analytic representation of improved IMFs IMF components are real signals, which are converted into an analytic form using Hilbert transform.
Analytic signals are suitable to find out instantaneous frequency and instantaneous amplitude of the signals. The analytic signal of mth IMF is defined as:
zm t em t jem t Am t e jm t
(7)
Where, Am t and m t are called instantaneous amplitude and the instantaneous phase angle, which can be defined as:
Am t
e t e t 2 m
2 m
and
em t em t
m t arctan
(8)
The instantaneous frequency of the signal is expressed as the rate of change of m t with respect to time
fm t
1 dm t 2 dt
(9)
The instantaneous frequency is the single-valued function of time [26].
EMG signal x(t)
IMF extracted after applying EMD c1(t)
c2(t)
MF
MF
d1(t)
d2(t)
……………
cK(t) MF
……………
dK(t)
Reconstructed filtered signal y(t)
Improved IMF extracted after applying EMD
e1(t)
e2(t)
…………….
eM(t)
Fig. 1. Block diagram of improved EMD 4.
Features extracted from improved IMFs
4.1 Bandwidth computation from analytic improved IMFs
The bandwidth of any signal provides information about the spread of frequency along the signal length. Signals may have the bandwidth due to amplitude modulation and due to large deviation in the instantaneous frequencies. These two bandwidth for analytic signal z t can be defined as:
2 2 d t 2 1 dA t B A t dt dt E dt dt 2
(10)
Here, E is the energy of analytic improved IMF and can be represented as [34]:
1 d t 2 A t dt E dt
(11)
From expression (10), it is clear that the bandwidth of analytic signal depends upon two components, first component is the amplitude and second component is the phase of the signal. From the above expression, bandwidth due to the amplitude modulation (BAM) and bandwidth due to the frequency modulation (BFM) can be represented as: 1 dA t dt E dt 2
BAM
(12)
1 d t A2 t dt E dt 2
BFM
(13)
4.2 Spectral moments of power spectral density (SMPSD) from analytic improved IMFs Power spectral density (PSD) is defined as the frequency response of any signal. It gives information about the distribution of average power in terms of frequency. PSD is suitable to find out power and dominant frequency of the signal. PSD of analytic signal z(t) can be defined as:
1 sz f lim T 2T
T
z t e
T
dt 2
j 2 ft
(14)
The first order spectral moment of PSD (SMPSD) provides information of higher order shape of the signal [35]. It can be represented as:
N
SM PSD k PSDk k 1
(15)
4.3 Mean of first derivative of instantaneous frequency (MFDIF) computation from analytic improved IMFs:
This feature is the first derivative of instantaneous frequency (MFDIF) that provides information about the difference between adjacent instantaneous frequencies of the signal. The mean of f can be represented as [36]:
N 1
MFDIF l 1
f (l ) N 1
where
f diff fi
(16)
Here, N is the number of samples of instantaneous frequency.
The least squares support vector machine (LS-SVM) classifier has been used for classification of ALS and normal EMG signals. The detailed description of LS-SVM classifier is available in [37-38]. 5.
Results and Discussion The presence of noise in EMG signal from various sources creates the changes in physical characteristics of
the signal. The noise in signal modifies the amplitude of signal for short duration and may present in entire range of frequency, due to which these noises can be considered as impulsive noise. Fig. 2 shows EMG signal with IMF components c1(t)-c8(t) and the residue rK(t) produced by EMD, before the median filtering. Due to the presence of impulse noise in EMG signal, mode mixing is present in IMF components, and the reasonable IMF components cannot be found through EMD. In the proposed method, EMD followed by the median filter is used to remove the impulse noise from IMF components, which are ultimately summed to generate the new filtered EMG signal. The filtered EMG signal is decomposed into improved IMF components through EMD process. Fig. 3 shows the filtered EMG signal and improved IMF components e1(t)-e8(t) with residue eM(t) induced by IEMD process. IMF components are arranged in decreasing order of the frequency and increasing order of IMF components. The median filtering is a robust way to eliminate the impulse noise from any signal. It is difficult to eliminate the noise completely, due to which the mode mixing may present in improved IMF components to some proportion. Median filtering of IMF components reduces the noise from EMG signals and improves the discrimination performance of the features. The discrimination results in Table 1-4 shows the effectiveness of median filtering in case of impulse noise in EMG signal. Table 1 shows the comparison of discrimination abilities of BAM feature in case of EMD, AFEEMD and proposed IEMD methods. It is clear from the Table 1 that the probability value is higher in case of EMD and AFEEMD methods as compared to IEMD method, which means that discrimination ability of BAM feature
extracted from IEMD method is better than EMD and AFEEMD methods. It is observed that the feature BAM of first four IMFs are statistically significant, which shows that first four IMF components have better discrimination ability. The feature BAM of IMFs for normal EMG signals is larger as compared to ALS EMG signals, it may be due to the rate of change of amplitude envelopes of IMFs is higher in normal EMG signals. Fig. 4 shows the discrimination performance of first four IMF components of feature BAM. Fig.4 (a) shows Kruskal-Wallis plot for EMD method and Fig. 4 (b) depicts Kruskal-Wallis plot for IEMD method. It is clear from visual inspection of plots that IEMD method is statistically significant for analysis of ALS and normal EMG signals. Table 2 depicts the discrimination performance of feature BFM in case of EMD, AFEEMD and improved EMD methods. From the table, it is clear that the probability value of feature BFM in case of proposed IEMD method is lower as compared to EMD and AFEEMD methods, which shows that feature BFM of IEMD method has better discrimination capability. Discrimination ability of first four IMFs is significantly better as compared to other IMFs. BFM
Fig. 5 shows Kruskal-Wallis plot of feature BFM
to describe the discrimination between ALS and normal of EMG signals. Fig. 5(a) shows the discrimination ability of feature BFM by using EMD method and Fig. 5(b) illustrates the discrimination ability of feature BFM by using IEMD method. Table 3 describes the discrimination ability of feature SMPSD in case of EMD, AFEEMD and IEMD methods. The value of probability is lower in case of IEMD method compared to EMD and AFEEMD methods, which shows the better discrimination performance of IEMD method. For the first four IMFs discrimination ability is significantly greater than other IMFs. The feature SMPSD of IMFs of ALS EMG signals is greater as compared to normal EMG signals. Fig. 6 shows the performance of EMD, and IEMD in case of SMPSD feature. Fig. 6(a) shows the performance of SMPSD feature using EMD method and Fig. 6(b) presents the performance of SMPSD feature using IEMD method. Table 4 exhibits the discrimination performance of feature MFDIF in case of typical EMD, AFEEMD and IEMD methods. From the probability values of the table, it is clear that the performance of proposed IEMD method is better than EMD and AFEEMD methods. Discrimination capability of first four IMFs component of IEMD method is higher as
to other IMFs. The feature MFDIF of IMFs for ALS EMG signals is larger
as compared to normal EMG signals. Fig. 7 shows the discrimination performance of MFDIF feature in case of
EMD, and proposed IEMD methods. Fig. 7(a) depicts the performance of MFDIF feature using EMD method and Fig. 7(b) shows the performance of MFDIF feature using proposed IEMD method. The probability value of the Table 1-4 clearly shows that the first four IMFs of all the features are statically significant as compared to all other IMF components. The features namely amplitude modulation bandwidth (BAM) and frequency modulation bandwidth (BFM) with spectral moments of power spectral density (SMPSD) and first derivative of instantaneous frequency (MFDIF) are used as an input features to the LS-SVM classifier with the redial basis function kernel. Table 5 shows the classification accuracy (%) of ALS and normal EMG signals classification using EMD, AFEEMD, and IEMD methods for first four IMFs. It can be seen from Table 5 that IEMD based features provided better classification accuracy of ALS and normal EMG signals as compare to EMD and AFEEMD. Hence the result presented in this paper shows the capability of proposed IEMD based features for diagnosis of ALS using EMG signals. 6.
Conclusion In this paper, we have demonstrated a new median filtering based improved EMD method for the
discrimination of ALS and normal EMG signals. The direct use of EMD cannot decompose the noisy signals efficiently due to the effect of impulse noise in the amplitude of the signals. The median filtering is a valuable tool to remove impulse noise from EMG signals. Therefore, the proposed method is capable of suppressing the impulse noise from EMG signals without losing any useful information. Thus, the use of median filter of different window size for each IMF components improves the filtering performance. The proposed IEMD method is strong enough for accurate decomposition of EMG signals containing impulse noise. The discrimination results after the processing of ALS and normal EMG signals demonstrate effectiveness of the proposed method. Four features BAM, BFM, SMPSD and MFDIF have been employed for the analysis of ALS and normal EMG signals. These parameters provide significant differences between ALS and normal EMG signals. The discrimination capability of the features is improved in IEMD method as compared to EMD and AFEEMD methods. Apart from these, the classification performance of proposed IEMD method is better as compare to exiting EMD and AFEEMD methods for diagnosis of ALS using EMG signals. The proposed method can be applied for the analysis of other non-stationary signals possessing the impulse noise.
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Fig. 2. Empirical mode decomposition of initial EMG signal x t
Fig. 3. Empirical mode decomposition of improved EMG signal y t
Table 1. Value of probability and mean ± std. of eight IMF components of BAM feature for EMD, AFEEMD and IEMD methods.
Methods
EMD
AFEEMD
IMF No.
Signal type
Mean ± std.
Probability
Mean ± std.
IMF1
ALS
0.057±0.0077
4.26×10-7
0.333±0.0866
IMF2
Normal ALS
6.72×10-7
0.3148±0.0789 0.1081±0.0392
IMF3
Normal ALS
0.0144±0.0073 0.0114±0.0106
Normal
0.0112±0.0069
ALS
0.0103±0.0095
IMF4
Normal ALS
IMF5
0.0102±0.009 0.0091±0.0067
ALS
0.0086±0.0069
Normal ALS
0.0087±0.0074 0.0101±0.0079
Normal
0.0084±0.0073
ALS
0.009±0.0077
Normal
0.0109±0.0073
IMF8
3.70×10
-4
2.14 ×10
-3
0.0106±0.0081
Normal IMF6
IMF7
0.0189±0.0077 0.012±0.0075
Probability 1.8×10-4
1.37×10
2.08×10
0.0437±0.0106
1.06×10-05
0.0188±0.0068
5.05×10
1.44×10
-1
3.87×10
-08
0.0123±0.007
0.1382±0.0532
6.05×10-8
0.174±0.0488 0.0535±0.0162
2.1×10-12
0.0676±0.0159 0.0262±0.0084
2.4×10-19
0.0351±0.0087 7.37×10-9
0.0224±0.0074 4.022×10-3
0.0139±0.0081 5.53×10
-02
0.0104±0.008
0.0156±0.0067 0.0124±0.0088
7.68×10
0.0095±0.0068 0.009±0.0068
4.96×10-1
-1
1.82×10-1
0.008±0.0066 9.28×10-1
Probability
0.0181±0.0082
0.0133±0.0058 -1
Mean ± std.
-1
0.1099±0.0326 0.0387±0.0129
0.0209±0.0058 -2
I-EMD
0.0117±0.0057 0.0084±0.0057
7.04×10-4
0.0103±0.0065
0.0086±0.0063
0.007±0.0049 8.76×10-1
0.009±0.0074
3.96×10-3
0.0088±0.0062
Table 2. Value of probability and mean ± std. of eight IMF components of BFM
feature for EMD,
AFEEMD and IEMD methods.
Methods IMF No. Signal type IMF1
IMF2
IMF3
IMF4
IMF5
IMF6
IMF7
IMF8
EMD Mean ± std.
Probability
3
ALS
1.33×10 ±358.36
Normal
8
5.65×10-6
1.52×10 ±349.71
ALS
646.87±213.77
Normal
705.85±175.85
ALS
AFEEMD
421.35±204.83
Normal
438.57±125.50
ALS
285.83±151.95
Normal
305.55±96.56
ALS
226.08±121.92
Normal
215.66±92.13
ALS
167.54±95.31
Normal
158.77±85.01
ALS
136.49±76.29
Normal
118.61±69.42
ALS
103.39±62.45
Normal
120.03±62.21
3.96×10-3
Mean ± std. 1.40×10
+04
1.42×10
+04
7.65×10
+02
I-EMD Probability
±2.96×10
+03
±3.32×10
+03
±1.72×10
+03
6.86×10
-01
1.359×10-3 1.81×10
-2
1.32×10 1.62×10
+03
±386.1291
4.22×10
5.54×10-09
2.18×10
322.8955±110.3514
7.6×10
7.52×10-1 1.25×10-1
3
3.25×103±1.25×103 1.68×103±671.32
4.75×10
1.14×103±477.53
2.6×10-11 1.6×10-11 5.20×10-6
3
1.47×10 ±588.44 7.73×10
-02
845.04±413.91
1.67×10-03
3
1.04×10 ±530.25
203.2098±82.8865 2.81×10-02 362.5539 81.9353 208.235±69.4117
566.59±268.02
150.5367±72.734 6.66×10-01 141.7612 62.9095 141.7612±62.9095 362.5539 81.9353
390.65±191.07
116.4382±61.2378
272.87±137.84
122.665±74.7709
3.69×10-7
2.28×10 ±741.38 -05
362.5539±81.9353 -1
4
8.99×10 ±3.36×10
3
667.1958±155.2054 -1
3
4.21×103±1.22×103
±478.6641
586.5573± 185.2538
Probability
3
1.11×10 ±3.07×10 -01
9.24×10+02±1.64×10+03 +03
Mean ± std.
9.96×10-01
1.72×10-02
691.58±369.1 2.24×10-02
487.99±280.36
329.65±216.58
3.96×10-03
Table 3. Value of probability and mean ± std. of eight IMF components of SMPSD feature for for EMD, AFEEMD and IEMD methods.
Methods IMF No. Signal type IMF1
ALS Normal
IMF2
ALS Normal
IMF3
ALS Normal
IMF4
IMF5
IMF6
IMF7
IMF8
ALS
EMD Mean ± std.
AFEEMD Probability
8
9
8
8
8
9
8
8
8
8
6.71×10 ±1.88×10
8.73×10-7
1.14×10 ±4.38×10 5.99×10 ±1.24×10
1.15×10-5
2.81×10 ±8.19×10 2.22×10 ±4.78×10
4 ×10
-04
1.43×108±2.98×108 8
8
4.24×10 ±8.88×10 8
2.08×10 ±4.71×10
ALS
3.71×108±6.23×108 8
3.18×10-5
2.42×10 ±4.84×10
ALS
8.18×108±2.08×109 8
1.42×10
+06
8.36×10
+06
5.72×10
+06
6.94×10
+07
2.66×10 8.68×10
1.32×10
-02
8
Normal
2.52×10
+06
Probability
±1.13×10
+07
±7.16×10
+06
±1.78×10
+07
±2.49×10
+07
±1.54×10
+08
2.17×10+07±4.48×10+07
8
Normal
Mean ± std.
3.49×10
9
+07
+4.36×10 ±2.24×10
+07
±1.18×10
+08
Normal
5.6×10 ±2.81×10
8.62×10
ALS
2.53×109±8.27×109
2.69×10+08±9.90×10+08
Normal
5.68×109±5.69×1010
ALS
5.06×1011±4.65×1012
Normal
9
3.89×10-06
±1.38×10
+08
7.54×10+07±1.67×10+08 2×10-03
10
9.07×10 ±6.42×10
1.15×10
±2.08×10
+08
6
6
6
2.61×10 ±1.42×10
1.88×10
1.02×10
-02
2.3×10-10
3.19×106±7.51×106 7
8.52×10-7
7
1.05×10 ±2.56×10 7
2.85×10-03
7
1.59×10 ±3.59×10
9.87×107±1.6×108 -02
6.14×10-6
7
8.37×107±3.6×108 2.22×10-02
9.69×10-5
1.25×10 ±8.91×10
3.68×107±7.42×107 6.10×10-05
7
3.49×10-5
8
4.87×10 ±1.52×10
1.98×108±4.96×108
2.22×10-04
7.66×107±1.42×108
3.50×10+08±8.53×10+08 +08
7
6.32×107±2.91×108 7.18×10-07
1.45×10+08±2.06×10+08 +07
Probability
6
1.09×107±4.53×107 1.75×10-05
+08 +08
Mean ± std. 9.25×10 ±6.87×10
4.74×10-03
1.65×10+08±2.16×10+08 7.57×10
-6
+08
I-EMD
2.73×108±5.15×108 1.60×10-01
3.96×10-03
1.4×108±2.59×108
Table 4. Value of probability and mean ± std. of eight IMF components of MFDIF feature for for EMD, AFEEMD and IEMD methods. Methods IMF No. Signal type IMF1
IMF2
IMF3
IMF4
IMF5
IMF6
IMF7
IMF8
ALS
EMD Mean ± std. 812.09±328.52
Normal
806.59±274.54
ALS
390.65±164.12
Normal
346.59±135.83
ALS
176.43±105.58
Normal
130.33±77.89
ALS
86.95±68.08
Normal
59.79±41.44
ALS
48.01±38.27
Normal
33.05±20.89
ALS
30.54±19.54
Normal
23.51±14.61
ALS
206.99±258.38
Normal
136.4±142.38
ALS
96.25±83.36
Normal
83.5±89.09
AFEEMD Probability 4.77×10
-01
Mean ± std. 1.19×10
+04
I-EMD Probability
±3.16×10
+02
1.28×10
-1
+04
2.74×10
5.20×10
-6
+03
5.2×10 ± 5.90×10 7.79×10
+02
2.17×10
+03
+02
±6.07×10
+02
±3.26×10
+02
1.00×10-4
8.60×10
-3
7.00×10 5.32×10
+02
9.60×10
1.09×10
±5.84×10
+01
±2.04×10
+01
±1.40×10
1.95×10
+01
5.26×10
±1.20×10
4.96×103±1.3×103
1.77×10-6
2.34×103±646.95
1.5×10-13
1.76×103±479.73 3.84×10-1
999.86±341.09
3.34×10-8
773.24±294.42 3.98×10
-2
446.87±245.55
2.64×10
-2
231.21±136.49
5.84×10
-1
1.15×10-5
347.25±170.5 8.73×10-6
177.11±129.14
+01
+01
6.67×10-6
4.2×10 ±955.2 -3
+01
2.09×10+01±1.28×10+01
1.01×10 ±1.06×10
3
+01
3.14×10+01±2.14×10+01 2.17×10
4.08×10-01
+02
6.06×10+01±3.83×10+01 3.90×10
6.64×10-05
±1.32×10
+02
1.87×10+02±7.55×10+01 1.27×10
-3
±1.52×10
+02
Probability 3
9.61×10 ±726.84 -2
1.87×10+03±3.18×10+02 +02
4
3
1.1503×10 ± 485.7054 -2
Mean ± std.
103.62±83.01
2.50×10-02
84.93±68.07 2.17×10-01
57.63±52.17 50.03±43.97
3.96×10-03
Table 5 Classification accuracy (%) of ALS and Normal EMG signals classification using for EMD, AFEEMD and IEMD methods. Kernel IMFs
EMD
AFEEMD
IEMD
(Parameters) IMF1 RBF (
1)
IMF2 IMF3 IMF4
89.91 92.66 91.74 88.99
90.47 91.74 90.47 85.71
92.66 96.33 94.49 90.47
Fig. 4. Comparison of BAM parameter for the four different IMF components of ALS and normal EMG signals (a) using typical EMD method, (b) using I-EMD method, and (c) using AFEEMD method.
Fig. 5. Comparison of BFM parameter for the four different IMF components of ALS and normal EMG signals (a) using typical EMD method, (b) using I-EMD method, and (c) using AFEEMD method.
Fig. 6. Comparison of SMPSD parameter for the four different IMF components of ALS and normal EMG signals (a) using typical EMD method, (b) using I-EMD method, and (c) using AFEEMD method.
Fig. 7. Comparison of MFDIF parameter for the four different IMF components of ALS and normal EMG signals (a) using typical EMD method, (b) using I-EMD method, and (c) using AFEEMD method.