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Denoising of ECG Signal with Power Line and EMG In- Terference Based on Ensemble Empirical Mode Decompo- Sition (Draft)

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Denoising of ECG Signal with Power Line and EMG In- Terference Based on Ensemble Empirical Mode Decompo- Sition (Draft) Denoising of ECG Signal with Power Line and EMG In- terference based on Ensemble Empirical Mode Decompo- sition (Draft) Shing-Hong Liu1, Li-Te Hsu2, Cheng-Hsiung Hsieh2, and Yung-Fa Huang3 1 Department of Computer Science and Information Engineering, Chaoyang University of Technology, Taichung, 41349, Taiwan, ROC. [email protected] 2 Department of Computer Science and Information Engineering, Chaoyang University of Technology, Taichung, 41349, Taiwan, ROC. 3 Department of Information and Communication Engineering, Chaoyang University of Tech- nology, Taichung, 41349, Taiwan, ROC. Correspondence author: [email protected] Abstract. In this paper, the mode decomposition (EMD) and ensemble empirical mode decomposition (EEMD) were used are used to perform a noise cancellation process on electrocardiogram (ECG) signal coupling the power line (PLn) and electromyogram (EMG) interference. The ECG signal with noise was decom- posed by the EMD or EEMD method. A series of intrinsic mode functions (IMF) were decomposed out. This was followed by the grey noise estimation method, which is used to perform noise estimation on the high-order IMF component. Then, determine whether the signal-to-noise ratio (SNR) of each IMF component was lower than the threshold values defined. These IMF components with lower SNR were removed, following which the ECG signal with the denosing process was obtained through reconstruction process. The performance evaluation on the noise cancellation method proposed was to use the ECG signals in the MIT-BIH cardiac arrhythmia database by adding the PLn and EMG noise to perform the processing. The results indicate that the EEMD method doing the noise cancel- lation had a better performance than EMD method. Keywords: ECG noise cancellation, ensemble empirical mode decomposition, grey system . 1 Introduction ECG is an important indicator in monitoring the cardiac activity measurements. During the measurement process of ECG signals, it is extremely vulnerable to various noises and artifact interferences, such as electromyogram (EMG), 50 or 60Hz power line noise, (PLn), baseline drift et al. In [1], it was found that the frequency of complex QRS wave of standard ECG signal is lower than 30Hz, and the peak of its spectrum is within the range between 4 and 12Hz. However, EMG and PLn belong to the high-frequency noises that are capable of completely hindering the characteristics of ECG, such that 2 QST wave cannot be detected precisely. Therefore, it is crucial to remove EMG and PLn noise in the ECG monitoring and clinical diagnosis. Traditional ECG noise reduction methods include the low-pass filter [2] to remove the high-frequency noises. In addition, high-frequency filter and adaptive filter are used for cancellation of low-frequency vibrations, such as baseline drift [3] and respiratory interference [4]. Since most of the noises in ECG are at the high-frequency bandwidth, the traditional low-pass filters cannot resolve the issue that signal and noise co-exist in the same bandwidth. The high-frequency noise of ECG signal usually were filtered by the frequency decomposition technique, such as the wavelet transformation method [5], EMD [6] and EEMD [7]. EMD is used to decompose ECG signal into numerous intrinsic mode function (IMF) components. As a result, it is a relatively important topic to find out the strength of noise energy in each IMF component when doing the denoising process. During the decomposition process of EMD, there are the problems of mode mixing. In one identi- cal IMF, there are noises of different bandwidth mixing with each other, or noises of the same bandwidth occur in different IMF compositions. To overcome the mode mix- ing problem in EMD, the method of EEMD [12] is a new white noise auxiliary data analysis method, which can be used to reduce the mod mixing effect with the next IMF scale. The frequency division for noise cancellation method of EEMD is widely used. For example, in Chang et al., to cancel the white noise in ECG, high-frequency noise was defined at the low-order IMF component. Thus, the low-order IMF components were excluded directly in order to denoise the ECG [13]. In Jenitta et al., the use of zero-crossing ratio of adjacent IMF components was proposed for the evaluation on whether the noise energy in IMF is too high in order to cancel the PLn noise in ECG [14]. Earlier research did not use each IMF component of ECG signal to predict their SNR ratio, but only directly used IMF 1 component as the basis for the noise cancellation process. However, when the SNR of ECG is too high, this method could denoise over and the reconstructed ECG signal could be the distortion. According to above descrip- tions, the goal of this research was to propose a method capable of performing the pre- diction the strength of the PLn and EMG noise of ECG signal in each IMF components. EMD and EEMD were used to get a series of IMFs. The grey noise estimation method was used to estimate the strength of the noises in each IMF component. Then, determine whether the SNR of the IMF component of each order was lower than the threshold values defined. If the IMF components have the lower SNR, they were not used to reconstruct the ECG signal. In this research, ECG signals were got from the MIT-BIH cardiac arrhythmia data- base, and the SNR improvement (SNR_imp) parameter is used to evaluate the perfor- mance of the noise cancellation technique proposed in this research on PLn and EMG noises. 3 2 Method Fig. 1 shows the architecture of the noise cancellation method proposed in this research. First, EMD or EEMD was used to decompose ECG signal with noise into a set of IMF components, following which grey noise estimation method is used to estimate the strength of noise energy of each IMF component, that is to calculate the standard devi- ation (SD), σ_|N ̂(f)| , of the estimated noise spectrum. If the SD is greater than the threshold value, 2.5e-5, it means that the SNR ratio of such IMF component is too low. This IMF would be excluded when reconstructing the ECG signal. EEMD was also the same process. The following provides further details on the noise cancellation method proposed. Fig. 1. Proposal of architecture of EEMD-EEM for the ECG signal noise cancellation method. 2.1 ECG signal In this research, the real ECG signals [17] from the cardiac arrhythmia database in the MIT-BIH database was used, mitdb / 100 and mitdb / 108. Each data includes a contin- uous period of 30 minutes, and the sampling frequency is 360Hz. After the ECG signal in the database is processed by the Butterworth filter of 0.3~40Hz, it is used as standard ECG signal, s(k). PLn and EMG noises were treated as noise sources and are embedded in the ECG signal. PLn noise bandwidth was generated by sinusoidal wave of 59.5 to 60.5Hz, and the sampling frequency was 360Hz. The EMG noise bandwidth was of 100 Hz to 500 Hz, and the sampling frequency was 1000Hz. The added noise is ex- pressed as n(k), and the ECG signal with noise is x(k), and the energy range of the added noise was from -5 to 15 dB, x (k) = s (k) + n (k). (1) SNR was defined as follows: 퐿−1 2 ∑푘=0 푠 (푘) 푆푁푅 = 퐿−1 2 , (2) ∑푘=0 푛 (푘) where L is the length of the signal. 2.2 EMD algorithm The EMD algorithm used in this research consists of the following steps: 4 Step1. Find the local maximum and minimum extremums in x(k). Step2. Connect the local maximum extremums and local minimum extremums into upper envelope and lower envelope respectively. Step3. Obtain the average of the upper and lower envelops as the average envelope m(k). Step4. Obtain the differential signal, d(k) = x(k) - m(k). Step5. If d(k) is a zeroing process, then stop the iteration and treat d(k) as the first IMF, which is called c1(k); otherwise, return back to Step (1), and use d(k) to replace x(k). Step6. Residual signal, r(k) = x(k) - c1(k). Step7. Use r(k) to replace x(k), and repeat the process from Steps (1) to (6) in order to obtain the Second IMF (IMF 2), which is called c2(k). To obtain 푐휋(k), after 휋 times of iteration, continue Steps (1) to (6). When the final residual signal, r(k), is obtained for the monotonic equation, then stop the processing. The original signal can be expressed as the following: 휋 푥(k) = ∑푖=1 푐푖(k) + 푟(푘), (3) where r(k) is typically considered as 푐휋+1(푘). 2.3 EEMD algorithm EEMD algorithm is as follows: Step1. Add the white noise sequence w(k) onto the target signal x(k), and 푥1(k) = x(k) + w(k). In this research, the addition of 5dB noise power is used. Step2. Use EMD algorithm to decompose 푥1(k), as described in Section 2.2. Step3. Repeat Steps (1) and (2) until the trial number of times predefined is complete. The repeated time each time is added onto the white noise series of the same power. New IMF combination 푐푖푗(k) is realized; where i refer to the iteration number, and j refers to IMF component. 2.4 Grey system noise estimation method In this section, the noise estimation technique based on the grey system is introduced. The construction process of GM(1,1) model was described in the references [18].. Then, GM(1,1) model was used to estimate noise (Grey noise estimation, GNE), and the 휎|푁̂(푓)| represented the noise strength.
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