De-noising surface electromyograms using an adaptive wavelet approach

Abstract

The recorded surface Electromyogram (sEMG) signals is inevitably influenced by noise during the signal acquisition process. Because of the constant deviation that is known as the Pseudo-Gibbs phenomenon, which exists in conventional wavelet threshold de-noising, noise pertaining to sEMG is inevitable. In order to avoid or minimize noise in the recorded sEMG signals, the objective of this study is to investigate the feasibility of developing a new de-nosing function that uses the advantage of the adaptive threshold adopted in the Brige-Massart algorithm and test the performance of the new function. The simulation results show that applying this new de-noising function could effectively remove noise in the recorded sEMG signals. Furthermore, when compared with conventional threshold de-noising function, the new function achieved higher performed de-noising effect, and thereby enabling better signal analysis subsequently.

Keywords

Surface electromyogram signal de-noising threshold function signal-to-noise ratio

1 Introduction

Surface Electromyogram (sEMG) signals recorded by the electrodes from the skin surface can reflect the weak bioelectric signals of the related activation of neuromuscular system [1]. It has been widely applied in the field of basic research, clinical medicine, rehabilitation medicine and sports medicine etc [2]. It is also well established that sEMG is a nonlinear and non-stationary signal [3]. In addition, its peak value is in the range of 0∼10 mV. However, the useful signal energy is very weak, which is generally in the range of 10 Hz∼50 Hz. During the process of collecting sEMG, a wide range of factors, such as the human body biological signals, the inherent noise of acquisition instruments, and the ambient noise, has a significant impact on the noise ratio of sEMG [4]. Due to the above mentioned features, sEMG de-noising has become a key issue in its data extraction implementation. Therefore, to remove the noise effectively and retain the useful weak sEMG signal is a crucial process.

The traditional de-noising method is designed according to the frequency range of sEMG signal filter, such as the Chebyshev filter, Kalman filter, etc. However, this filtering process is complicated and difficult to realize, and its effect is not obvious. Kale utilized the artificial neural network method to remove the noise in the sEMG signal [5]. However, the artificial neural network method has its problems in this field of signal processing research [6]. At the same time, the selection of weight uncertainty results in migration to the local extremity and instability. The Fourier transform plays an enormous role in the process of the steady state signal de-noising. For stationary signals, the Fourier transform method applied to de-noising can achieve the ideal effect, but sEMG signals from the acquisition of human body pertain to non-stationary signaling. Due to the limitation of Fourier transform, it is unable to characterize the sEMG signal of local time-frequency characteristics and influences the de-noising effect. Wavelet transform is the inheritance and development of the Fourier transform. It is a new time-frequency analysis method with time frequency localization and multi-resolution, which can be effective to de-noising of non-stationary signal. Therefore, many scholars have applied the wavelet transform to the de-noising of sEMG [7 –9].

At present, there are many de-noising methods based on the wavelet analysis [10, 11], such as the wavelet transform modulus maxima de-noising algorithm that is proposed by Mallat [12], the spatial correlation to noise algorithm that is proposed by Xu et al. [13], and application of another wavelet threshold used in de-noising that is proposed by Donoho et al. [14]. Evidently, the wavelet threshold in de-noising algorithm is common. This method can achieve the best estimated value in Besov space and a better convergence in comparison with the other methods [14]. The processing method is simple and little computation. So it is widely used in the field of de-noising [15 –17]. In practical applications, it is common to use hard thresholding function or soft threshold function for de-noising signals. The hard threshold function appears readily in the pseudo Gibbs phenomena and many unexpected signal peaks, and result in loss of smoothness of the original signal because of its signal reconstruction. Although the soft threshold function has good continuity, there always exists a constant bias between the estimated value and the actual value. Besides, the derivative of soft threshold function is not continuous and has certain limitations [18]. Some literatures [19–20] adopts the improved wavelet threshold function pertaining to the sEMG signal de-noising in order to overcome the hard and soft threshold de-noising problems, which achieves good results. For example, Chen Guiliang et al. put forward a new method in 2013. It is called μ rhythm threshold method which is provided to improve threshold function [21]. The method can solve the effect to the threshold treatment of the soft-threshold wavelet coefficients constant deviation. Meanwhile, the application of the method in the wavelet analysis shows that wavelet packet μ rhythm method de-noising significantly are better than wavelet μ rhythm threshold method. However, the form of improved threshold function is complex. The parameter value of threshold function is determined through a series of tests for the computational complexity, large amount of calculation, which is often not good enough for signal reconstruction.

In order to resolve the issues presented the above algorithm, this paper proposes a new threshold function and sets the Signal-to-Noise Ratio (SNR) as the performance index. We can obtain an optimal threshold function by selecting a suitable value of parameter a and combining the adaptive threshold value of Brige-Massart algorithm for de-noising sEMG. The experimental results show that this method has a good performance during de-noising of the sEMG, In addition, it cannot only further improve the Signal-to-Noise Ratio (SNR), but also reduce the Root-Mean-Square Error (RMSE) in comparison with the traditional methods. In addition, this research is important in the field of bio-signal processing as its ability to improve the data accuracy and reliability used for diagnosis.

2 Methods

2.1 The basic principle of wavelet transform

We note that ψ (t) ∈ L² (R), and $\hat{ψ} (\bar{w})$ is Fourier transform. If $\hat{ψ} (\bar{w})$ meets the permitted conditions, we have: $C_{ψ} = \int_{R} \frac{{| \overset{\land}{ψ} (\bar{w)} |}^{2}}{| w |} dw < \infty .$ (1) Then, ψ (t) is called the basic wavelet or the mother wavelet. After translating and scaling the ψ (t), we can obtain: $ψ_{a, b} (t) = \frac{1}{\sqrt{| a |}} ψ (\frac{t - b}{a}) a, b \in R; a \neq 0 .$ (2)

The formula (2) is called wavelet series. Here, a is the expansion factor, and b is the translation factor. For an arbitrary function f (t) ∈ L² (R), its wavelet transform is: $W_{f} (a, b) = < f, Ψ_{a, b} > = {| a |}^{- 1 / 2} \int_{R} f (t) Ψ (\frac{t^{-} - b}{a}) dt .$ (3)

The reconstruction formula is: $f (t) = \frac{1}{C_{ψ}} \int_{R} \int_{R} \frac{1}{a^{2}} W_{f} (a, b) ψ (\frac{t - b}{a}) dadb$ (4)

2.2 sEMG de-noising principle based on wavelet threshold method

In Wavelet de-noising, a sEMG model with noise can be expressed as: $f (t) = s (t) + n (t) .$ (5)

In the above formula, s (t) is the original signal, and n (t) is Gaussian white noise whose variance is σ² and obeys the distribution of N (0, σ²). The steps for Wavelet thresholding and de-noising are as follows:

Wavelet decomposition: Choosing the suitable wavelet base function, and making sure we have the right number j, which is the level number of decomposing wavelet. The coefficients ω_j,k of decomposing wavelet can be obtained when the sEMG signal are decomposed to the jth level.

Threshold Processing: This step includes threshold and threshold function. The decomposing coefficients is dealt by threshold, and then quantified. The rule of quantification is called the threshold function.

Wavelet reconstruction: The reconstruction signal can be obtained through inverse of the quantified wavelet decomposing coefficients, which is the denoised sEMG. As an exemplification, the sEMG wavelet threshold de-noising process is shown in Fig. 1.

Fig.1

sEMG wavelet threshold de-noising process.

From the wavelet thresholding process, there exist four factors that can influence the de-noising effects: the select of wavelet basic function and decomposition layers number j, rules of choosing threshold and the design of threshold function, which is the key point to denoise wavelet thresholding [20]. The SNR and the RMSE can be regarded as the evaluation metric for de-noising effects, whereby the SNR value is proportional to the effects. On the contrary, the lower the RMSE value, the better is the coincidence degree. Their relationships are shown as follows:

$SNR = 10 log \begin{matrix} \end{matrix} (\frac{\sum_{n = 1}^{N} s^{2} (n)}{\sum_{n = 1}^{N} {[s (n) - \hat{s} (n)]}^{2}}),$ (6) $RMSE = \sqrt{\frac{1}{N} \sum_{n = 1}^{N} {[s (n) - \hat{s} (n)]}^{2}},$ (7) where s (n) is the original signal, $\hat{s} (n)$ is the reconstruction signal that is denoised, and N is the sample length.

2.3 The selection of threshold and threshold function

2.3.1 Threshold selection

Determining the threshold size is the key issue of wavelet thresholding process. If the threshold is too small, part of the noise will be viewed as useful signal to be reserved, which can cause the “over reservations” phenomenon. On the contrary, if the threshold is too large, part of the useful signal will be filtered out as noise, and the “over strangle” phenomenon will emerge. Traditional threshold always use the Sqtwolog Donoho-Johnstone [22], but usually this thresholding signal is overly smooth and easily misses the important information of original signal. This study adopts a multi-threshold algorithm, which is based on Birge-Massart, and takes a different threshold for each decomposed signal. The Birge-Massart algorithm is defined by three parameters, which is j, M and a [23]:

If the decomposition level is greater than the sub-levels j, all the coefficients should be retained.

The largest absolute value coefficient n_I for level j is given by:

n_{i} = \frac{M}{(j + 2 - i)^{a}} a > 1 .

(8)

We note that M and a are the experience coefficients, and j is the decomposition level. Generally, M is the length of coefficients after decomposing the first level. The coefficient a is 1.5 when compression Birge-Massart algorithm is used, and the coefficient a is 3 when de-noising. The threshold is c (n_i) after computing n_I, which bases on the absolute value of wavelet coefficients in descending order.

2.3.2 Threshold function selection

Threshold function is the criteria of wavelet coefficients. Traditional threshold function includes soft threshold function and hard threshold function, which reflects the different treatment strategies of wavelet coefficients [22]. We assume that W_j,k is the wavelet coefficient of wavelet decomposition and ${\hat{W}}_{j, k}$ as the wavelet coefficient threshold for de-noising, as well as T is the threshold.

Hard threshold function: The coefficients, which are less than the threshold T, are assigned to zeros. Otherwise they are kept unaltered. This can be expressed as:

{\hat{W}}_{j, k} = {\begin{matrix} W_{j, k} \\ 0 \end{matrix} \begin{matrix} | W_{j, k} | \geq T \\ | W_{j, k} | < T \end{matrix},

(9)

Soft threshold function: The coefficients, which are higher than threshold, are reduced by an amount to the value of threshold. Otherwise they are set to zeros. This can be expressed as:

{\hat{W}}_{j, k} = {\begin{matrix} sign (W_{j, k}) (| W_{j, k} | - T) \\ 0 \end{matrix} \begin{matrix} | W_{j, k} | \geq T \\ | W_{j, k} | < T \end{matrix},

(10)

In this formula, the sign (n) pertains to the sign function as follows: $sign (n) = {\begin{matrix} 1 \\ - 1 \end{matrix} \begin{matrix} n > 0 \\ n < 0 \end{matrix}$ (11)

Fig.2

Threshold function.

From the definition of soft and hard threshold functions, we can see that in general, the good signal edges and other local features can be retained by the hard threshold method. But as shown in Fig. 2 (a), due to the hard threshold function, there exists the discontinuity in – T and T, so that the reconstruction easily generates the local oscillation and leads to a smooth signal reconstruction. The soft threshold function is relatively smooth and its continuity is good compared with hard threshold function. But there is a certain deviation between ${\hat{W}}_{j, k}$ and W_j,k, which can cause the fuzzy edge distortion phenomenon, and significant signal loss in terms of its characteristics. Therefore, the hard threshold and soft threshold functions have their limitations. Given the shortcomings of the traditional soft and hard threshold function, this paper proposes a new wavelet threshold function: ${\hat{W}}_{j, k} = {\begin{matrix} sign (W_{j, k}) (| W_{j, k} | - \frac{4 a}{π} T {arccot}^{1 - a}) \\ 0 \end{matrix} \begin{matrix} | W_{j, k} | \geq T \\ | W_{j, k} | < T \end{matrix} .$ (12)

In this formula, a ranges from 0 to 1. When setting a as 0, (12) becomes the hard threshold function of (9). When taking a as 1, (12) becomes soft threshold function of (10), and in general, when a ∈ (0, 1), the ${\hat{W}}_{j, k}$ estimated value lies between the soft and hard thresholds. Therefore, the new threshold function has continuity and decreases the deviation between ${\hat{W}}_{j, k}$ and W_j,k. The threshold function preserves the advantages of the two kinds of traditional threshold function and make up their shortcomings and deficiencies in processing of wavelet coefficients. This function is flexible and convenient with a good de-noising effect.

Since the purpose of algorithm is to achieve a minimum of $| {\hat{W}}_{j, k} - U_{j, k} |$ , therefore, if the |W_j,k| value is between |W_j,k| - T and |W_j,k|, the wavelet coefficients ${\hat{W}}_{j, k}$ after treatment would be closer to U_j,k. We note that U_j,k corresponds to the true signal wavelet coefficients in the wavelet threshold de-noising algorithm. Therefore, in Equation (12), a can be seen as an independent variable and the measure of de-noising effect of SNR as a function of a based on this idea. Finally, in order to get the best de-noising effect, maximum SNR is made by the corresponding a. The basic flow of improved wavelet threshold de-noising is shown in Fig. 3.

Fig.3

Basic flow chart of improved wavelet threshold de-noising.

3 Experimental results

3.1 sEMG collection

The sEMG signal acquisition process as shown in Fig. 4. The sEMG is extracted by the surface electrodes, which are affixed onto the skin, and they are input into the data acquisition card of DAQ, which are then enlarged through the signal conditioning equipment filter amplifier. Finally, the signal is collected with the digital form and transmitted to the computer via the A/D conversion.

Fig.4

sEMG acquisition process.

When collecting the signal, the subject’s right hand palm lay flat on the desktop and he/she repeated the process of clenching his fist forcibly and then slowly releasing this action at the regular interval. The collected signal was then processed and its output as the sEMG signal, which was then processed by the data acquisition card. In this experiment, the sampling frequency is 1000 Hz, and there are 20 groups, whereby each group has 2000 points. Finally, the discrete sampling value of SEMG signal is conducted based on the signal threshold de-noising algorithm using the Matlab software. The collection experiment is shown in Fig. 4.

3.2 sEMG de-noising

Figure 5 shows the fist signal from the flexor carpi ulnaris of a healthy male subject that is programmed by the MATLAB software. Because of the noise is not obvious, in order to judge the effect of several de-noising methods better, the author adds Gauss white noise according to the characteristics of EMG signal noise. The resulting noise signal is shown in Fig. 6. In our experiment, we used the sym4 as the mother wavelet according to the sEMG signal de-noising effect. The choice of wavelet decomposition layer has a great influence on the de-noising result. The large number of layers can filter the useful signal together with noise. A small number is unable to filter this noise effectively. According to the practical experience, we will decompose the number of layers to two layers, and the threshold value is obtained through the Birge-Massart penalty function strategy. The change curve between the noise ratio of new threshold function and the independent variable a is shown in Fig. 7.

Fig.5

Original sEMG.

Fig.6

Noisy sEMG.

Fig.7

Graph of SNR versus a.

In Fig. 7, the SNR is the unimodal function of a in de-noising resulting about the new threshold function. There exists a maximum point that SNR is higher than hard threshold function when a = 0 and SNR is higher than soft threshold function when a = 1. Using an optimizing function, the maximized SNR value can be found.

In the MATLAB 2010 environment, the added noise signal is denoised by the universal threshold of Donoho-Johnstone [22], the soft threshold function, the hard threshold function, and a new threshold function. Then, the characteristics of de-noising is performed by the SNR and RMSE. Three experimental results about de-noising method are shown in Fig. 8, and the SNR and RMSE are shown in Table 1.

Fig.8

Six methods of de-noising results contrasting figure.

Table 1

Six types of algorithm of de-noising effect data tables

De-noising Method	Signal to Noise Ratio	Root Mean Square Error
	(SNR)	(RMSE)
Universal threshold + Soft threshold de-noising	38.662	0.0465
Universal threshold + Hard threshold de-noising	39.1388	0.0454
Universal threshold + New threshold de-noising	40.6101	0.0422
Birge-Massart Punishment strategy+ Soft threshold de-noising	41.7665	0.0398
Birge-Massart Punishment strategy+ Hard threshold de-noising	40.3764	0.0426
Birge-Massart Punishment strategy+ New threshold de-noising	42.3448	0.0387
(a = 0.592)

4 Discussion and conclusion

In this study, we investigated a new threshold de-noising function, which combines the adaptive threshold of the Brige-Massart algorithm, to remove noise in sEMG effectively. From Fig. 8 we can show that the sEMG of de-noising effect that utilizes the new threshold function and the Birge-Massart Punishment strategy is better than the joint de-noising, which combines universal threshold, soft threshold function and hard threshold function de-noising. Our experimental results show that the method has a good performance during de-noising of the sEMG,. Besides, it can not only further improve the Signal-to-Noise Ratio (SNR), but also reduce the Root-Mean-Square Error (RMSE) in comparison with the traditional methods with the new threshold function in the Table 1. This method is mainly manifested in small signal attenuation, whereby the rich details and more useful signals can be retained. Although our experimental results can achieve the higher SNR and lower RMSE while comparing other method, we will focus on the using non-parameter approach to get the adaptive threshold de-noising function in future studies.

The acquisition of sEMG signal is very complex, and it is very important that this signal is preprocessed as the procedure is easily disturbed by noise, which leads to a low signal-to-noise ratio. For the study of EMG signal de-noising, the wavelet function has been widely used. An improved threshold function of wavelet denoising method is proposed in this paper in order to remove the noise in the signal. In order to obtain the optimal threshold function, the parameters of the threshold function are adjusted adaptively according to the signal to noise ratio by making full use of the characteristics of the wavelet. Then, combined with adaptive threshold of Brige-Massart calculation method, this sEMG signal can be de-noised. Compared with the traditional threshold methods, the de-noising effect of new method is more obvious. It can effectively suppress the noise in the signal and significantly improve the signal-to-noise ratio. This paper will be useful in the field of physiotherapy. It can be used to develop patients with muscle control problems. The framework from this research may even be used to develop controllable prosthetics or to build exoskeletons. Also, this method can be widely used in the study of weak signal de-noising.

Conflict of interest statement

We confirm that all authors of this manuscript have no conflicts of interest to declare.

Footnotes

Acknowledgments

Key University Science Research Project of Anhui Province, China (Project KJ2016A813), Anhui Provincial Natural Science Foundation (Project 1708085MF164).

References

De Luca

C.J.

, Physiology and mathematics of myoelectric signals, IEEE Trans Biomed Eng 26(6) (1979), 313–325.

Wang

, The assessment study of electrically evoked muscle fatigue based on myoelectric signals, In: Peking Union Medical College Thesis (5) (2013).

, Zhu

and Luo

, De-noising method of the sEMG based on EEMD and second generation wavelet transform, Chin J Sens Actuators 25(11) (2012), 1488–1493.

Yaohang

, Lesheng

, Jihong

, et al., A methodological approach to remove the ECG noise from the EMG signals, IEEE 2011 10th International Conference on Electronic Measurement and Instruments 3 (2011), 228–331.

Kale

S.N.

and Dudul

S.V.

, Intelligent noise removal from EMG signal using focused time-lagged recurrent neural network, Applied Computational Intelligence and Soft Computing (2009), Article ID 129761.

Kaushik

, Sinha

H.P.

and Dewan

, Biomedical signals analysis by DWT signal de-noising with neural networks, Res J Appl Sci 9(5) (2014), 244–256.

Wang

J.H.

, Chen

, Xiao

, et al., Wavelet-based neural network adaptive filter for sEMG denoising, Appl Mech Mater 121–126 (2011), 4259–4264.

, Yin

, Jin

J.N.

, Li

, et al., Feasibility of surface electromyo graphy signal acquisition for action recognition, J Clin Rehabil Tissue Eng Res 15(22) (2011), 4103–4106.

Wissam

, Rachid

, et al., An efficient algorithm of ECG signalde-noising using the adaptive dual threshold filter and thediscrete wavelet transform, Biocybern Biomed Eng 36(3) (2016), 499–508.

10.

Tanu

and Karan

, EMG classification wavelet functions to determine musclecontraction, J Med Eng Technol 40(3) (2016), 99–105.

11.

Supuk

T.G.

, Skelin

A.K.

and Cic

, Design, development and testing of a low-cost sEMG system and its use in recording muscle activity in human gait, Sensors 14(5) (2014), 8235–8258.

12.

Mallat

and Hwang

W.L.

, Singularity detection and processing with wavelets, IEEE Trans Inf Theory 38(2) (1992), 617–643.

13.

Y.S.

, Weaver

J.B.

, et al., Wavelet transform domain filters: A spatially selective noise filtration technique, IEEE Trans Image Process 3(6) (1994), 747–758.

14.

Donoho

D.L.

, De-noising by soft-thresholding, IEEE Trans Inf Theory 41(3) (1995), 613–627.

15.

Gradolewski

, Tojza

, et al., Arm EMG wavelet-based de-noising system, Adv Intell Syst Comput 317 (2015), 289–296.

16.

Kasambe

P.V.

and Rathod

S.S.

, VLSI wavelet based denoising of PPG signal, Procedia Comput Sci 49 (2015), 282–288.

17.

Wang

and Fan

Y.F.

, Denoising of sEMG signal based on wavelet threshold shrinkage, Comput Simul 27(2) (2010), 325–327.

18.

Kong

, Super Learing Manual of MATLAB Wavelet Analysis. Posts & Telecom Press, Beijing, 2014.

19.

Hong

, Ye

and Meng

, Application of new threshold-noising method in EMG processing, Mechan Electr Eng Mag 26(10) (2009), 90–93.

20.

Chen

and Sun

, Adaptive de-noising of pulse signal based on multiple wavelet transform, Electron Meas Technol 31(8) (2008), 120–122.

21.

Chen

, Wang

and Liu

, EMG signal de-noising based on wavelet packet rhythm threshold method, Appl Mech Mater 394 (2013), 560–565.

22.

Liang

, Cai

, Li

, et al., Scale-invariant v-transform signal de-noising, Chin J Comput 36(9) (2013), 1929–1942.

23.

Zhang

, et al., MATLAB Wavelet Analysis. China Machine Press, Beijing, China, 2010.