Denoising of Electrocardiogram (ECG) signal by using empirical mode decomposition (EMD) with non-local mean (NLM) technique

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Available online at www.sciencedirect.com

ScienceDirect journal homepage: www.elsevier.com/locate/bbe 1 2 3

Original Research Article

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Denoising of Electrocardiogram (ECG) signal by using empirical mode decomposition (EMD) Q1 with non-local mean (NLM) technique

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Q2

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Q3 Department of Electrical Engineering, NIT Rourkela, India

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Shailesh Kumar, Damodar Panigrahy *, P.K. Sahu

article info

abstract

Article history:

In this paper, the investigation on effectiveness of the empirical mode decomposition (EMD)

Received 25 August 2017

with non-local mean (NLM) technique by using the value of differential standard deviation

Received in revised form

for denoising of ECG signal is performed. Differential standard deviation is calculated for

16 January 2018

collecting information related to the input noise so that appropriate formation in EMD and

Accepted 29 January 2018

NLM framework can be performed. EMD framework in the proposed methodology is used for

Available online xxx

reduction of the noise from the ECG signal. The output of the EMD passes through NLM

Keywords:

the EMD process. The performance of the proposed methodology has been validated by

Electrocardiogram (ECG) signal

using added white and color Gaussian noise to the clean ECG signal from MIT-BIH arrhyth-

framework for preservation of the edges and cancel the noise present in the ECG signal after

Empirical mode decomposition

mia database at different signal to noise ratio (SNR). The proposed denoising technique

(EMD)

shows lesser mean of percent root mean square difference (PRD), mean square error (MSE),

Non local mean (NLM) technique

and better mean SNR improvement compared to other well-known methods at different

R peak detection methodology

input SNR. The proposed methodology also shows lesser standard deviation PRD, MSE, and SNR improvement compared to other well-known methods at different input SNR. © 2018 Nalecz Institute of Biocybernetics and Biomedical Engineering of the Polish Academy of Sciences. Published by Elsevier B.V. All rights reserved.

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Introduction

Electrocardiogram (ECG) signal is used to extract information related to physiology of the heart. In reality, various noise sources are interfered with the ECG signal [1]. This noise incorporates muscle artifacts, high frequency noise, electrode contact noise, baseline wander, and powerline interference. To

extract the correct information related to physiology of the heart, the cancelation of the noise present in the ECG signal is needed. The correct detection and delineation of P wave and T wave are required to identify atrial fibrillation, increasing chance of sudden cardiac death. In ECG signal, P wave and T wave are mostly affected by various noise sources due to their amplitudes. For detection and delineation of P wave and T

* Corresponding author at: Department of Electrical Engineering, NIT Rourkela, India. E-mail addresses: [email protected] (S. Kumar), [email protected] (D. Panigrahy), [email protected] (P.K. Sahu). https://doi.org/10.1016/j.bbe.2018.01.005 0208-5216/© 2018 Nalecz Institute of Biocybernetics and Biomedical Engineering of the Polish Academy of Sciences. Published by Elsevier B.V. All rights reserved. Please cite this article in press as: Kumar S, et al. Denoising of Electrocardiogram (ECG) signal by using empirical mode decomposition (EMD) with non-local mean (NLM) techniqueQ1. Biocybern Biomed Eng (2018), https://doi.org/10.1016/j.bbe.2018.01.005

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wave the edges the ECG signal in the denoised process should be preserved. Different signal processing technique have been proposed to cancel the noise from the ECG signal. Different techniques for denoising of the ECG signal are Wiener filter (WF) [2], adaptive filtering technique [3,4], bandpass filtering [5], wavelet denoising (WD) [6–8], principal component analysis [9], neural network [10], extended Kalman filter (EKF) [11], empirical mode decomposition (EMD) [12,13], nonlocal mean technique (NLM) [14]. Wiener filter is applied in stationary signal to minimize the mean square error. Wiener filter [2] has been used for cancelation of noise from the ECG signal. The methodology does not require extra sensor signal with the noisy ECG signal. The filtering methodology does not provide good performance for cancelation of noise from the noisy ECG signal, as the behavior of the ECG signal is non-stationary. Adaptive filtering technique [3,4] has been used for cancelation of noise like motion artifact, electromyogram (EMG), powerline interference, and baseline wander noise. This filtering methodology requires a reference signal with noisy ECG signal. The efficiency of the methodology reduces due to the error in the reference signal. Bandpass filtering technique [5] has been also used for cancelation of noise from the ECG signal. This methodology provides not good performance for removal of noise from the ECG signal, as it is unable to suppress non-cardiac ECG noise added with ECG signal. Infinite impulse response (IIR) Gaussian recursive filter [15] has also been used for removal of noise from the ECG signal. This algorithm is used for real-time application and provides fast operation. The performance is medium. A graphic processing unit (GPU) parallel algorithm based on NLM methodology [16] has been used for denoising of the ECG signal. It is used for real-time diagnosis. This methodology provides faster operation for denoisng of the ECG signal with similar result of NLM methodology. A real time ECG denoisng method based on recursive filter [17] has been proposed. The methodology denoises the ECG signal based on boundary condition. This methodology does not require higher computational operation. This methodology is used for real time visualization. Different wavelet denoising techniques [6–8] have been used for cancelation of the noise from the ECG signal. The wavelet denoising techniques cancel the noise from the ECG signal. The wavelet denoising techniques cancel the noise by using the characteristic of noise in the frequency domain. This methodology requires thresh holding with some shrinkage rule for cancelation of the noise. These methodology fail to preserve the edges of the ECG signal. Principal component analysis [9], neural network [10] have been also used for removal of the noise from the ECG signal. These methodologies require multiple leads to provide good performance by using co-relation operation, as in case of single channel noisy ECG signal, these methodologies do not provide good performance for noise cancelation from the ECG signal. Extended Kalman filter (EKF) [11], extended Kalman smoother (EKS) [11], unscented Kalman filter (UKF) [11] have been used for cancelation of the noise from the ECG signal. These methodologies used synthetic dynamic model with

exact R peak detection for cancelation of the noise. These methodologies provide good performance for cancelation of the noise, but these methodologies sometimes require operator interaction depend upon the noisy ECG signal for proper initialization of parameters of EKF, EKS or UKF. Empirical mode decomposition (EMD) [12,13] has been also used for removal of the noise from the ECG signal. This methodology uses EMD operation by preserving QRS complex with Turkey window. This methodology reduces noise but cannot completely remove the noise from the ECG signal. Nonlocal mean technique [14] also has been used for cancelation of the noise from the ECG signal. This technique uses average operation in the neighborhood for cancelation of the noise. As the methodology depends upon the width of the neighborhood, and it is fixed for all noisy ECG signal. So in noisier ECG signal, the performance of the NLM technique is not good. Most of the denoising techniques [2–6,9,10] cannot provide edge preserving of the ECG signal. EKF/extended Kalman smoother (EKS) technique [11] preserves the edge, but it sometimes requires the operator interaction depending upon the noisy ECG signal. EMD technique [13] reduces the noise from the ECG signal, but cannot remove the total noise from the ECG signal. NLM technique [14] preserves the edges but it strongly depends upon the local width and half width of neighborhood, and it is fixed for all the noisy ECG signal. So the performance of the NLM tecnique decreases as the noise in the signal increases. To give better performance than NLM and EMD with preserving edge authors have proposed a new methodology using NLM with empirical mode decomposition (EMD) by using different standard deviation for cancelation of the noise from the ECG signal. The EMD framework is used in the proposed approach to reduce the noise from the ECG signal. The main aim of this work is to preserve the edges of the ECG signal with lesser percent root mean square difference (PRD), mean square error (MSE), and better SNR improvement for cancelation of the noise from the ECG signal. The organization of the paper is as follows: The proposed methodology based on empirical mode decomposition (EMD) with non-local mean (NLM) using differential standard deviation is explained in Section 2. The results and discussion are presented in Sections 3 and 4 respectively. Final section (conclusion section) presents the conclusion.

2.

Proposed methodology

The proposed methodology using empirical mode decomposition (EMD) with non-local mean (NLM) framework by using value of the differential standard deviation to cancel the noise from ECG signal is displayed in Fig. 1. The proposed methodology for cancelation of the noise from the ECG signal consists of four stages namely R peak detection, differential standard deviation calculation, empirical mode decomposition (EMD) framework, and non-local mean (NLM) framework. In the R peak detection stage, the R peak of the ECG signal is detected. The standard deviation of mean amplitude of the ECG signal is subtracted from standard deviation of the ECG signal to calculate the differential standard deviation, in the

Please cite this article in press as: Kumar S, et al. Denoising of Electrocardiogram (ECG) signal by using empirical mode decomposition (EMD) with non-local mean (NLM) techniqueQ1. Biocybern Biomed Eng (2018), https://doi.org/10.1016/j.bbe.2018.01.005

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2.2.

Fig. 1 – Schematic representation of proposed methodology (EMD + NLM) for cancelation of noise and preservation of edges from the ECG signal.

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differential standard deviation calculation stage. In the EMD framework stage, the noise present in the ECG signal is canceled by EMD with the help of differential standard deviation. In the final stage (NLM framework stage), the output of the EMD is passed through NLM to preserve the edge of the ECG signal and also cancel the noise from the ECG signal after the EMD framework stage. The detail description of each stage is presented in following subsections.

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Stage 2: Differential standard deviation calculation

The objective of this stage is to compute the differential standard deviation by using detected R peaks of the ECG signal. This calculated differential standard deviation is used in EMD as well as NLM framework for denoising of the ECG signal. The differential standard deviation is calculated by subtracting the standard deviation of mean amplitude of the ECG signal from the standard deviation of the ECG signal. The standard deviation of mean amplitude of the ECG signal is calculated by computing the mean amplitude of the ECG signal. For computation of the mean amplitude of the ECG signal phase assignment is required. The detected R peaks are used for assignment of phase. Phase assignment is linear warping between two consecutive R peaks. The procedure for assignment of phase is explained in [19–21]. Fig. 2 shows assigned phase and normalized noise ECG data. The formula used for calculation of the normalized ECG signal (normalized ECG noisy data) is as follows:

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Normalized ECG signal 193 192

Stage 1: R peak detection

The objective of this stage is to identify the R peaks of the ECG signal. This detected R peaks will help to compute the differential standard deviation of the ECG signal, which is used in EMD as well as NLM framework for the denoising approach. This detected R peaks also help to detect QRS complex in the EMD framework. A four stage improved R peak detection method based on Shannon energy [1,18] is used in this manuscript to detect R peaks of the ECG signal, which displays average sensitivity of 99.95%, positive predictive value 99.88% and average accuracy of 99.84% using first channel of all the dataset of MIT-BIH arrhythmia database (MITDB) [1]. The used R peak detection methodology does not need the amplitude threshold, and prior detected R peaks. The four stage based improved R peak detection methodology based on Shannon energy envelope displays better detection of R peaks by using varying amplitude of ECG signal (varying amplitude of R peak, P peak and T peak), varying QRS morphology, low amplitude of ECG, noisy ECG, time varying ECG, long pause ECG signal compared to well-known existing methodology [1].

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ECG signal ¼ Maximum amplitude of the ECG signal After the phase assignment process, mean phase is calculated, and the mean amplitude is calculated using the mean phase. Both the mean amplitude of the ECG signal and mean phase of the ECG signal consist of sampling frequency number of samples. The mean phase of the ECG signal consists of sampling frequency number of samples evenly spaced between p to p. The procedure to calculate the mean amplitude of ECG signal (finding mean of amplitude corresponding to mean phase (the procedure for calculation of mean amplitude of ECG signal is presented in [22,23])) is explained as follows: The average of amplitude value of the samples, whose assigned phase values are p is considered as initial (first) sample of the mean amplitude of the ECG signal. The following description is the process to calculate values of the mean amplitude of the ECG for second sample to end of the sample (value of sampling frequency). Initially, sample locations are estimated by using the assigned phase, and ECG signal in between the desired phase value range, the desired

Fig. 2 – Assignment of phase by using added white Gaussian noise at 5 dB input SNR to first channel of 106 data numbered MITDB. Please cite this article in press as: Kumar S, et al. Denoising of Electrocardiogram (ECG) signal by using empirical mode decomposition (EMD) with non-local mean (NLM) techniqueQ1. Biocybern Biomed Eng (2018), https://doi.org/10.1016/j.bbe.2018.01.005

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phase value range lies between the phase value of previous sample and corresponding sample of the mean phase of the ECG. The mean value of the amplitude of the ECG signal correspond to the estimated sample locations, is the value at the corresponding value of the mean amplitude of the ECG signal. The example to explain the procedure to calculate the mean amplitude of ECG at corresponding sample is presented follow. The procedure to estimate the mean amplitude of the ECG at third sample is presented as below: The value of mean phase of ECG correspond to third sample 358p and second sample are 356p 360 , 360 MIT-BIH is used in this approach, sampling frequency of MIT-BIH database is 360 Hz, so, here sampling frequency = fs = 360, Let us assume, at locations 450, 451, 453, 670, 671, 672, 810, 811, 812, 1215, 1216, 1217 the phase value of the ECG signal is more than 358p 360 (previous sample (third sample)) and less than or equal to 358p 360 (corresponding sample (second sample)). Finally, the mean amplitude ECG corresponds to third sample value is average of amplitude values correspond to the estimated samples (450, 451, 453, 670, 671, 672, 810, 811, 812, 1215, 1216, and 1217) from the ECG signal. As this is average process so that possibility that noisy portion is reduced. The figure indicating mean phase and mean amplitude using the noisy ECG signal is shown in Fig. 3. Finally the differential standard deviation (dSD) is calculated by subtracting standard deviation of the mean amplitude of the ECG

signal from standard deviation of the ECG signal. The equation of the dSD is as follows:

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dSD ¼ standard deviation ðmean amplitude of ECGÞ 247 246 standard deviation ðECGÞ

(1)

2.3. Stage 3: Empirical mode of decomposition (EMD) framework The objective of this stage is to reduce the noise of the ECG signal using the detected R peaks and the different standard deviation value. Empirical mode decomposition decomposes the signal in to a sum of intrinsic mode functions (IMFs). An IMF is subtraction of lower and upper envelope by interpolation using local maxima and minima of the signal [24]. The number of IMFs by using noisy ECG signal is shown in Fig. 4. The EMD framework for reduction of the noise in the ECG signal consists of three steps: Step-1 is selection of number of IMFs for delineation of QRS complex using different standard deviation. Step-2 is used for delineation of QRS complex with help of the predicted R peaks of the ECG signal. Step-3 is used for preserving the QRS complex by windowing methods, and reduce the noise from the noisy ECG signal using IMFs. Step-1: The objective of this step is to identify the addition of number of IMFs so that QRS complex can be delineated and

Fig. 3 – Mean phase and mean amplitude of added white Gaussian noise at 5 dB input SNR to first channel of 106 data numbered MITDB.

Fig. 4 – (a) Original ECG signal from first channel of 106 data numbered MITDB with 5 dB SNR using white Gaussian noise, (b)– (h) EMD decomposition of the ECG signal using 1–7 IMFs respectively. Please cite this article in press as: Kumar S, et al. Denoising of Electrocardiogram (ECG) signal by using empirical mode decomposition (EMD) with non-local mean (NLM) techniqueQ1. Biocybern Biomed Eng (2018), https://doi.org/10.1016/j.bbe.2018.01.005

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preserved. Generally the QRS complex present in higher frequency in the ECG signal. So first 1 to 3 number of IMFs are selected or added to get a signal which consists of QRS complex with noise. By experimentation, we have obtained the number of IMFs ( n) to be selected for addition of IMFs according to the differential standard deviation (dSD) weight is as follows: 8 for dSD > 0:2 <3 n¼ 2 for 0:2  dSD > 0:0710 : 1 for 0:0710  dSD > 0:0150

(2)

Step-2: The main aim of this step is to delineate QRS complex or detect Q and S point using detected R peaks. Here we calculate the sum of IMFs (d) obtained in step-1 is as follows:

282 d¼

n X Si ðtÞ

(3)

i¼1

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n, number of IMFs selected for detection of QRS complex in step-1; Si is the ith IMF of the ECG signal using EMD method. Two nearest zero crossing point from detected R peak location of the sum of IMFs is QRS boundary of the ECG signal. Thus QRS boundary of the ECG signal is preserved. Step-3: In this stage, Tukey window is used to preserve the QRS boundary. This will help to preserve the edge as well as reduce the noise from the ECG signal. Only first several IMFs correspond to noise. The Tukey window (tapered cosine window) is used here for preserving the QRS complex and eliminate other components of the signal. The window function for Tukey window is as follows [25]: 8    1 jtjt 1 > > < 1 þ cos p t 2 t1 wðtÞ ¼ 2 > >1 : 0

for t 1 jtjt 2 jtj < t 1 jtj > t 2

(4)

Here t1, standing boundary location of QRS complex (time instant); t2, ending boundary location of QRS complex. The Tukey window for the noisy ECG signal is shown in Fig. 5. Then using this windowing and other IMFs the formula for reduction of noise from the ECG signal is [13]:

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n n n X X X si ðtÞwðtÞ þ 0:05ð1wðtÞÞsi ðtÞ þ si ðtÞ þ rN ðtÞ yðtÞ ¼ i¼1

i¼1

(5)

i¼1

Here y(t), output of EMD framework (reduction of noise from the ECG signal); si(t), ith number of IMF of the using EMD; w(t), Tukey windowing output using delinated QRS boundary; n, number of IMFs selected in step-1; N, total number of IMFs present; rN(t), residue at Nth instant using EMD. Finally, noise is reduced from the ECG signal using EMD framework. The output of EMD framework of the proposed methodology using noisy ECG signal is shown in Fig. 7(c).

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2.4.

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Stage 4: Non local mean (NLM) framework

The main aim of this stage is to preserve the edge of the ECG signal as well as to remove the noise from the ECG signal which passed through EMD framework of the proposed methodology. The NLM technique denoises the signal by averaging the different regions with similar characteristics [26]. For a given sample se, the estimated denoised ECG signal at that sample (output of NLM framework (sig(se))) is a weight sum of values at other points t that are with in some search neighborhood Ne(se). The pictorial representation to estimate the output of NLM at sample instant se using search neighborhood is Ne(se) is shown in Fig. 6. The formulation for denoising of ECG signal using NLM is as follows [14]:

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Fig. 5 – (a) Added white Gaussian noise at 5 dB SNR to first channel of 106 data numbered MITDB, (b) representation of Tukey window of added white Gaussian noise at 5 dB SNR to first channel of 106 data numbered MITDB.

Fig. 6 – Representation of parameters of NLM to estimate output of NLM framework at sample instant se. Please cite this article in press as: Kumar S, et al. Denoising of Electrocardiogram (ECG) signal by using empirical mode decomposition (EMD) with non-local mean (NLM) techniqueQ1. Biocybern Biomed Eng (2018), https://doi.org/10.1016/j.bbe.2018.01.005

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332 Output of NLM framework ¼ sigðseÞ ¼ 333 334 335

Where ZðseÞ ¼

336

P

0 weðse; tÞ

B B ¼ expB B @

t weðse; tÞ

X deD

X 1 weðse; tÞyðtÞ ZðseÞ t 2 NeðseÞ

(6)

and weights are [14] !1

ðyðse þ dÞyðt þ dÞÞ2 C C C C 2LD l2 A

3. (7)

 2  dt ðse; tÞ  exp 2LD l2 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355

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Here l, bandwidth parameter; y(t), output of EMD framework; sig(se), denoised ECG signal; we(se,t), weights; dt, summed, squared point by point difference between samples in the patch centered at seand t; D, local patch of samples surrounding at se sample; LD, number of samples surrounding at se sample. The selection of values for the NLM framework is important. The performance of the NLM technique depends upon LD. LD defined as 2P + 1. Here P = half width. The P is shown in Fig. 6. So, the performance of the denoising technique depends upon the half width. Here, the P is set according to the value of the differential standard deviation. By experimentation, we have obtained the relationship between P and dSD. The formulation for P according to differential standard deviation (dSD) is as follows: 8 < 15 for dSD > 0:2 P ¼ 10 0:2  dSD > 0:0710 : 8 0:0710  dSD > 0:0150

are distorted after denoising by using EMD with NLM framework as shown in Fig. 7(d). In 2nd, 3rd and 5th cycle the edges of T wave is completely distorted by the addition of noise as shown in Fig. 7(b), but using EMD with NLM framework the edge of T wave is recovered in 2nd, 3rd and 5th cycle with little bit distortion as shown in Fig. 7(d).

(8)

Here l = 0.6 (standard deviation of ECG signal). Finally we have got sig(se), the denoised ECG signal. The output of EMD and NLM framework of the proposed methodology is shown in Fig. 7. The amplitude of P wave in 2nd and 5th cycle are very small as shown in Fig. 7(a), as the P wave in these 2 cycle completely covered by the noise and difficult to identify after addition of noise to the ECG signal as shown in Fig. 7(b), so edges of P wave

Results

The first channel of data numbered as 215, 115, 106, 105, 103, 100 from the MIT-BIH arrhythmia database (MITDB) [27] are used to compute performance of the proposed methodology. MITDB has 48 records, and each record has two channels. In this database the sampling frequency is 360 Hz. The data numbered as 215 was collected from male having age of 81, it is normal sinus rhythm with heart rate 81–124. The data numbered as 115 was collected from female having age of 39, it is normal sinus rhythm with heart rate 50–84. The data numbered as 106 was collected from female having age of 24, it is normal sinus rhythm with heart rate 49–87. The data numbered as 105 was collected from female having age of 63, it is normal sinus rhythm with heart rate 78–102. The data numbered as 103 was collected from male, age was not recorded, and it is normal sinus rhythm with heart rate 62–92. The data numbered as 100 was collected from male having age of 69, it is normal sinus rhythm with heart rate 70–89. The colored Gaussian noise added noisy ECG signal and the white Gaussian noise added noisy ECG signal are generated at different input SNR for performance evaluation of the proposed methodology. The procedure used to generate the noise (colored Gaussian noise and white Gaussian noise) at particular input SNR as elaborated in the manuscript [11]. The colored Gaussian noise and white Gaussian noise at particular input SNR (in between 5 dB (decibel) to 20 dB) is added to the actual ECG signal to generate colored Gaussian noisy ECG signal and white Gaussian noisy ECG signal respectively at the particular SNR. The result section is divided into two sub sections namely qualitative analysis, and quantitative analysis. In qualitative analysis sub section the output of the proposed denoising methodology is compared with the output of other techniques for denoising of ECG signal such as conventional filtering [5], adaptive filtering [4], non-local mean

Fig. 7 – Output of NLM framework of proposed methodology by using first channel of 106 data number of MIT-BIH arrhythmia database (a) original ECG signal, (b) noisy ECG signal by adding white Gaussian noise at 5 dB input SNR, (c) output of EMD framework of proposed methodology, (d) output of NLM framework of the proposed methodology. Please cite this article in press as: Kumar S, et al. Denoising of Electrocardiogram (ECG) signal by using empirical mode decomposition (EMD) with non-local mean (NLM) techniqueQ1. Biocybern Biomed Eng (2018), https://doi.org/10.1016/j.bbe.2018.01.005

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(NLM) [14], wavelet soft threshold denoising [6], and empirical mode decomposition (EMD) [13]. In quantitative analysis subsection, mean square error (MSE), percent root mean square difference (PRD), and SNR improvement of the proposed denoising methodology is compared with PRD, MSE, and SNR improvement of other techniques for denoising of ECG signal such as conventional filtering, adaptive filtering, wavelet soft threshold denoising, non-local mean (NLM), and empirical mode decomposition (EMD). The proposed methodology is implemented in MATLAB R 2014A.

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Fig. 8 displays the comparison of different ECG noise cancelation methods for cancelation of noise from added colored noise to the first channel of 106 data number of MITDB at 5 input SNR. Fig. 9 displays the comparison of different ECG noise cancelation method for cancelation of noise from added white noise to the first channel of 100 data number of MITDB at 5 dB input SNR. All the figures in qualitative subsection (Figs. 8 and 9) display that the proposed methodology (EMD + NLM) shows less distortion compared other ECG denoising techniques, and display nearly similar result as the original ECG signal. The EMD technique require few initial samples (transient period) to provide better result for denoising of the ECG signal, in the transient period there is a possibility of reduction of amplitude of the ECG signal using EMD, so the amplitude of the first R peak in EMD denoisning and EMD with NLM denoising is reduced as shown in Fig. 9(g) and (h). In between 5th and 7th cycle the ECG signal is normal as sow in Fig. 9(a), but after addition of noise the baseline drift happens in between 5th and 7th cycle as shown in Fig. 9(b). As EMD,and EMD with NLM methodology is used to cancel the noise but not for correction of baseline drift (two stage median filter can be used to correct the baseline drift), in between 5th and 7th cycle in Fig. 9(g) and (h) shows baseline drift.

Qualitative analysis

3.2.

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Quantitative analysis

The performance of the different noise cancelation technique of the ECG signal is evaluated by calculating mean square error (MSE), percent root mean square difference (PRD), SNR improvement (SNRimp). The formulas for calculating these parameters is represented as follows [22]: "P

N ðyðnÞxðnÞÞ2 SNRimp ¼ 10log10 P n¼1 2 N Ã n¼1 ðxðnÞsxðnÞÞ N X 1 2

#

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MSE ¼

ðxÃðnÞxðnÞÞ N n¼1 vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi uPN 2 u ðxÃðnÞxðnÞÞ PRD ¼ 100t n¼1 PN 2 n¼1 x ðnÞ

where y, noisy ECG signal; N, number of samples presented in clean ECG signal; xÃ, estimated clan ECG signal by the denoising technique, x, clean ECG signal.

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Each noise cancelation method has been run 50 times at each input SNR values for the performance evaluation purpose. Fig. 10(a) shows EMD + NLM method gives better SNR improvement compared to other methodologies such as conventional filtering, adaptive filtering, wavelet soft thresholding, NLM, EMD for cancelation of added white Gaussian noise at 5 dB to 20 dB input SNR to ECG signal. And it shows nearly same improvement of SNR as wavelet soft thresholding technique for added white Gaussian noise at 20 dB input SNR to the ECG signals. Fig. 10(b) shows EMD + NLM method gives lesser standard deviation of SNR improvement compared to other methodologies such as conventional filtering, adaptive filtering, wavelet soft thresholding, NLM, EMD for cancelation of added white Gaussian noise at different input SNR (5 dB to 20 dB) to the ECG signal. Table 1 shows EMD + NLM method gives lesser MSE compared to other methodologies such as conventional filtering, adaptive filtering, wavelet soft thresholding, NLM, EMD for denosing of added white Gaussian noise at 5 dB to 20 dB input SNR to the ECG signals.

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Fig. 8 – Output of various ECG noise cancelation technique for cancelation of added color noise to 106 from MITDB at 5 dB SNR. (a) Original (clean) ECG signal, (b) noisy ECG signal, (c) conventional filtering, (d) adaptive filtering, (e) wavelet soft threshold denoising, (f) NLM technique, (g) EMD technique, (h) EMD + NLM methodology.

Please cite this article in press as: Kumar S, et al. Denoising of Electrocardiogram (ECG) signal by using empirical mode decomposition (EMD) with non-local mean (NLM) techniqueQ1. Biocybern Biomed Eng (2018), https://doi.org/10.1016/j.bbe.2018.01.005

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Fig. 9 – Output of various ECG noise cancelation technique for cancelation of added white noise to 100 from MITDB at 5 dB SNR. (a) Original (clean) ECG signal, (b) noisy ECG signal, (c) conventional filtering, (d) adaptive filtering, (e) wavelet soft threshold denoising, (f) NLM technique, (g) EMD technique, (h) EMD + NLM methodology.

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Table 2 shows EMD + NLM method gives lesser standard deviation of MSE compared to other existing techniques such as conventional filtering, adaptive filtering, wavelet soft thresholding, NLM, EMD for denosing of added white Gaussian noise at different input SNR (5 dB to 20 dB) to the ECG signal.

Fig. 11(a) shows EMD + NLM method gives lesser PRD compared to other methodologies (conventional filtering, adaptive filtering, wavelet soft thresholding, NLM, EMD) for cancelation of added white Gaussian noise at 5 dB to 20 dB input SNR to the ECG signals.

Fig. 10 – (a) Mean SNR improvement of conventional filtering, adaptive filtering, wavelet denoising, NLM, EMD, proposed methodology (EMD + NLM) for cancelation of added white Gaussian noise at different SNR to different ECG signal. (b) Standard deviation of SNR improvement of conventional filtering, adaptive filtering, wavelet denoising, NLM, EMD, proposed methodology (EMD + NLM) for cancelation of added white Gaussian noise at different SNR to different ECG signal.

Please cite this article in press as: Kumar S, et al. Denoising of Electrocardiogram (ECG) signal by using empirical mode decomposition (EMD) with non-local mean (NLM) techniqueQ1. Biocybern Biomed Eng (2018), https://doi.org/10.1016/j.bbe.2018.01.005

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Table 1 – Mean MSE of conventional filtering, adaptive filtering, wavelet denoising, NLM, EMD, proposed methodology (EMD + NLM) for cancelation of added white Gaussian noise at different input SNR to different ECG signals. Technique/input SNR (dB) Conventional filtering Adaptive filtering Wavelet denoising NLM EMD EMD + NLM

5

0

5

10

15

20

0.046575 0.019476 0.007851 0.017821 0.017337 0.00769

0.017025 0.017366 0.003193 0.003945 0.00609 0.003099

0.007403 0.009927 0.001311 0.001152 0.002501 0.001021

0.004414 0.006762 0.000514 0.000853 0.001256 0.000472

0.003516 0.005667 0.000212 0.000356 0.000825 0.000117

0.003214 0.004636 8.69E-05 0.0003 0.000703 0.0000265

Table 2 – Standard deviation of MSE of conventional filtering, adaptive filtering, wavelet denoising, NLM, EMD, proposed methodology (EMD + NLM) for cancelation of added white Gaussian noise at different input SNR to different ECG signals. Technique/input SNR (dB) Conventional filtering Adaptive filtering Wavelet denoising NLM EMD EMD + NLM

489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524

5

0

5

10

15

20

0.022361 0.00735 0.004309 0.008741 0.008193 0.003979

0.008406 0.005964 0.001663 0.001934 0.002677 0.001429

0.003835 0.005458 0.000678 0.000589 0.00122 0.000509

0.002539 0.004982 0.000288 0.00034 0.00068 0.000282

0.002212 0.004427 0.000224 0.000275 0.000531 0.000217

0.002075 0.004181 0.00021 0.000254 0.000542 0.000212

Fig. 11(b) shows EMD + NLM method gives lesser standard deviation of PRD compared to other techniques (conventional filtering, adaptive filtering, wavelet soft thresholding, NLM, EMD) for cancelation of added white Gaussian noise at 5 dB to 20 dB input SNR to the ECG signals. Table 3 shows EMD + NLM method gives lesser MSE compared to other methodologies such as conventional filtering, adaptive filtering, wavelet soft thresholding, NLM, EMD for denosing of added color Gaussian noise at 5 dB to 20 dB input SNR to the ECG signals. Table 4 shows EMD + NLM method gives lesser standard deviation of MSE compared to other methodologies such as conventional filtering, adaptive filtering, wavelet soft thresholding, NLM, EMD for denosing of added color Gaussian noise at 5 dB to 20 dB input SNR to the ECG signals. Fig. 12(a) shows EMD + NLM method gives better SNR improvement compared to other methodologies such as conventional filtering, adaptive filtering, wavelet soft thresholding, NLM, EMD for cancelation of added color noise at 0 dB to 20 dB input SNR to the ECG signals. And it shows nearly same improvement of SNR as wavelet soft thresholding technique for denoising of added color noise at 20 dB input SNR to the ECG signals. Fig. 12(b) shows EMD + NLM method gives lesser standard deviation of SNR improvement compared to other methodologies such as conventional filtering, adaptive filtering, wavelet soft thresholding, NLM, EMD for cancelation of added color noise at 0 dB to 20 dB input SNR to the ECG signals. Fig. 12(c) shows EMD + NLM method gives lesser PRD compared to other methodologies (conventional filtering, adaptive filtering, wavelet soft thresholding, NLM, EMD) for cancelation of added color noise at 5 dB to 20 dB input SNR to the ECG signals. And it shows nearly same PRD as wavelet soft thresholding technique for cancelation of added color noise at 20 dB input SNR to the ECG signals.

Fig. 12(d) shows EMD + NLM method gives lesser standard deviation of PRD compared to other methodologies (conventional filtering, adaptive filtering, wavelet soft thresholding, NLM, EMD) for cancelation of added color noise at 5 dB to 20 dB input SNR to the ECG signals. And it shows nearly same PRD as wavelet soft thresholding technique for cancelation of added color noise at 20 dB input SNR to the ECG signals. The white Gaussian noise is generated at different input SNR using 100 number dataset of MIT-BIH arrhythmia database 50 times and generate 50 different sets of added white Gaussian noise to the 100 number dataset of MIT-BIH arrhythmia database. The performance of the proposed methodology for removal of using these datasets is shown Q4 in Figs. 18–20. Fig. 13(a) shows EMD + NLM method gives better SNR improvement compared to other methodologies (conventional filtering, adaptive filtering, wavelet soft thresholding, NLM, EMD) for cancelation of added white Gaussian noise at 5 dB to 20 dB input SNR to the first channel of 100 number data set of MITDB ECG signal. And it shows nearly same improvement of SNR as wavelet soft thresholding technique for cancelation of added white Gaussian noise at 20 dB input SNR to the ECG signal (first channel of 100 dataset of MITDB). Fig. 13(b) shows EMD + NLM method gives lesser MSE compared to other methodologies (conventional filtering, adaptive filtering, wavelet soft thresholding, NLM, EMD) for cancelation of added white Gaussian noise at 5 dB to 20 dB input SNR to the ECG signal (first channel of 100 dataset of MITDB). Fig. 13(c) shows EMD + NLM method gives lesser PRD compared to other methodologies such as conventional filtering, adaptive filtering, wavelet soft thresholding, NLM, EMD for cancelation of added white Gaussian noise at 5 dB to 20 dB input SNR to the first channel of 100 number data set of MITDB ECG signal. And it shows nearly same PRD as wavelet soft thresholding technique at 20 dB input SNR.

Please cite this article in press as: Kumar S, et al. Denoising of Electrocardiogram (ECG) signal by using empirical mode decomposition (EMD) with non-local mean (NLM) techniqueQ1. Biocybern Biomed Eng (2018), https://doi.org/10.1016/j.bbe.2018.01.005

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Fig. 11 – (a) Mean PRD of conventional filtering, adaptive filtering, wavelet denoising, NLM, EMD, proposed methodology (EMD + NLM) for cancelation of added white Gaussian noise at different SNR to different ECG signal. (b) Standard deviation of PRD of conventional filtering, adaptive filtering, wavelet denoising, NLM, EMD, proposed methodology (EMD + NLM) for cancelation of added white Gaussian noise at different SNR to different ECG signal. Table 3 – Mean MSE of conventional filtering, adaptive filtering, wavelet denoising, NLM, EMD, proposed methodology (EMD + NLM) for cancelation of added color Gaussian noise (pink noise) at different SNR to different ECG signal (using 100,103, 104, 105, 106, 115, 215 from MIT-BIH arrhythmia database). Technique/input SNR (dB) Conventional filtering Adaptive filtering Wavelet denoising NLM EMD EMD + NLM

561 562 563 564 565 566 567 568 569 570 571 572

5

0

5

10

15

20

0.041146 0.019589 0.06927 0.05693 0.06680 0.0552

0.0169391 0.0143297 0.0213799 0.0168214 0.0206884 0.014683

0.007257 0.00968836 0.0069638 0.0056767 0.0071500 0.005238

0.0044493 0.0066498 0.0022492 0.0019923 0.0027506 0.001804

0.0035999 0.00567025 0.0007284 0.0008265 0.0013031 0.000749

0.0033535 0.00466577 0.0002335 0.0004456 0.0009087 0.0003008

Fig. 14(a) shows that the proposed methodology (EMD + NLM) shows better SNR improvement compared to other techniques such as conventional filtering, adaptive filtering, wavelet soft thresholding, NLM, EMD for cancelation of added white Gaussian noise at 5 dB SNR to by using different data number of MITDB. Fig. 14(b) shows that the proposed methodology (EMD + NLM) shows lesser MSE compared to other techniques for cancelation of added white Gaussian noise at 5 dB SNR to different data number of MITDB. Fig. 14(c) shows that the proposed methodology (EMD + NLM) shows lesser PRD compared to other technique such as

conventional filtering, adaptive filtering, wavelet soft thresholding, NLM, EMD for cancelation of added white Gaussian noise to different dataset of MITDB at 5 dB SNR.

573 574 575

4.

576

Discussion

The noise cancelation in the ECG signal is important to get a clear ECG signal, so that pathological information related to heart can correctly extracted. Various methodologies have been used for removal of the noise from the ECG signal. These methodology are adaptive filtering [4], wavelet soft thresh-

Please cite this article in press as: Kumar S, et al. Denoising of Electrocardiogram (ECG) signal by using empirical mode decomposition (EMD) with non-local mean (NLM) techniqueQ1. Biocybern Biomed Eng (2018), https://doi.org/10.1016/j.bbe.2018.01.005

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Table 4 – Standard deviation of MSE of conventional filtering, adaptive filtering, wavelet denoising, NLM, EMD, proposed methodology (EMD + NLM) for cancelation of added color Gaussian noise at different SNR to different ECG signal. Technique/input SNR (dB) Conventional filtering Adaptive filtering Wavelet denoising NLM EMD EMD + NLM

582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628

5

0

5

10

15

20

0.018126 0.007895 0.033009 0.028002 0.032056 0.026655

0.009059 0.006015 0.009863 0.007588 0.009295 0.007242

0.003517 0.005545 0.003361 0.002921 0.003449 0.002892

0.002684 0.005284 0.001069 0.000992 0.001302 0.000978

0.002279 0.005432 0.000349 0.000464 0.000727 0.000341

0.002171 0.005394 0.000112 0.000312 0.000608 0.000106

olding technique [6], non-local mean (NLM) denoising [14], conventional filtering (band pass filter) [5], empirical mode decomposition (EMD) [13]. As shown in qualitative analysis subsection the proposed methodology (EMD + NLM) gets very similar result as original ECG signal and very less distortion with preserving edges compared to adaptive filtering, non-local mean (NLM) denoising, wavelet soft thresholding technique, and conventional filtering (band pass filter) for removal added colored Gaussian noise, and white Gaussian noise to the ECG signal. The reason behind preserving of edges of the ECG signal in the proposed methodology for removal of added different noises is due to the use of NLM technique, as NLM technique preserves the edges of the ECG signal by averaging the similar reasons. The proposed methodology (EMD + NLM) shows better performance (lesser MSE and PRD and better SNR improvement) compared to other technique as shown in the quantitative analysis subsection. The reason for better performance are appropriate detection of R peaks, determination of exact number of IMFs required for windowing operation in the EMD technique, and computation of exact value of the width of the local neighborhood of the NLM technique. In the proposed methodology, the appropriate R peak detection is required for calculation of differential standard deviation, preserving the QRS complex in the EMD technique. The computation of differential standard deviation is used for determination of exact number of IMFs required for windowing operation in the EMD technique, and computation of exact value of the width of the local neighborhood of the NLM technique. In the proposed methodology, a four stage improved method using Shannon energy based R peak detection is used to detect R peaks of the ECG signal. The R peak detection methodology used in this paper shows better performance for detection of R peaks compared to other existing methods as shown in [1]. As the used R peak detection technique shows better performance in noisy ECG signal, so the proposed methodology shows better performance for denoising of the ECG signal. The differential standard deviation is calculated by subtracting the standard deviation of mean amplitude of the ECG signal from the standard deviation of the ECG signal. The standard deviation of the mean of the ECG signal provides the standard deviation of the denoisined ECG signal for one cycle, because the mean of the ECG signal is sum of the ECG signal for each cycle by using assigned phase value (phase value is calculated by detected R peaks) provides a mean denoised ECG signal for a cycle. The subtraction of standard deviation of

mean amplitude of the ECG signal from the standard deviation of the ECG signal provides the information related to the noise. So at different input SNR the differential standard deviation value varies. BY using the differential standard deviation value assignment of exact number of IMFs required for windowing operation in the EMD technique, and exact value of the width of the local neighborhood of the NLM technique is performed. Due to the exact assignment these values in EMD and NLM provides better performance. In the proposed methodology EMD is used to reduce the noise. As we have observed from the literature, the ECMD technique generally used for reduction of noise from the ECG signal. We have also observed from the literature that, NLM technique provides better performance at higher input SNR. The output of the EMD provides higher input SNR for the input to the NLM framework. So in the proposed methodology output of the EMD, passes through NLM frame work with proper assignment of width of the local neighborhood provides better performance. Due to the above reasons the proposed methodology shows lesser mean MSE and mean PRD and better mean SNR improvement compared to all the other techniques as shown in qualitative analysis subsection. It also shows lesser standard deviation of MSE, standard deviation of PRD and standard deviation SNR improvement compared to all the other techniques, which indicates the proposed methodology provides less deviation. The proposed methodology (EMD + NLM) shows lesser MSE and PRD and better SNR improvement compared to EMD and NLM because the proposed method uses the differential standard deviation value to get information related to input SNR so that number of IMFs for windowing of EMD and width, and half width of the local neighborhood can be varied which strongly depend upon the input SNR where as in EMD, and NLM technique these values are fixed. Due to this reason the proposed methodology (EMD + NLM) shows lesser MSE, and PRD, and better SNR improvement compared to EMD and NLM. In the proposed methodology (EMD + NLM), EMD reduces the noise from the noisy ECG signal, so that NLM techniques further reduces the remaining noise, and preserve the edges also. The proposed methodology (EMD + NLM) also shows lesser PRD, and MSE and better SNR improvement compared to other techniques of denoising of white and color noise added ECG signal as shown in quantitative analysis subsection. The proposed methodology (EMD + NLM) framework suggests that it can be used for denoising of the ECG signal. The results of this work have recommended that the clinical

Please cite this article in press as: Kumar S, et al. Denoising of Electrocardiogram (ECG) signal by using empirical mode decomposition (EMD) with non-local mean (NLM) techniqueQ1. Biocybern Biomed Eng (2018), https://doi.org/10.1016/j.bbe.2018.01.005

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Fig. 12 – (a) Mean SNR improvement of conventional filtering, adaptive filtering, wavelet denoising, NLM, EMD, proposed methodology (EMD + NLM) for cancelation of added color Gaussian noise at different input SNR to different ECG signal. (b) Standard deviation of SNR improvement of conventional filtering, adaptive filtering, wavelet denoising, NLM, EMD, proposed methodology (EMD + NLM) for cancelation of added color Gaussian noise at different input SNR to different ECG signal. (c) Mean PRD of conventional filtering, adaptive filtering, wavelet denoising, NLM, EMD, proposed methodology (EMD + NLM) for cancelation of added color Gaussian noise at different input SNR to different ECG signal. (d) Standard deviation of PRD of conventional filtering, adaptive filtering, wavelet denoising, NLM, EMD, proposed methodology (EMD + NLM) for cancelation of added color Gaussian noise at different input SNR to different ECG signal.

Please cite this article in press as: Kumar S, et al. Denoising of Electrocardiogram (ECG) signal by using empirical mode decomposition (EMD) with non-local mean (NLM) techniqueQ1. Biocybern Biomed Eng (2018), https://doi.org/10.1016/j.bbe.2018.01.005

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Fig. 13 – (a) Mean SNR improvement of conventional filtering, adaptive filtering, wavelet denoising, NLM, EMD, proposed methodology (EMD + NLM) for cancelation of added white Gaussian noise at different input SNR to 100 number dataset of MITDB ECG signal. (b) Mean MSE of conventional filtering, adaptive filtering, wavelet denoising, NLM, EMD, proposed methodology (EMD + NLM) for cancelation of added white Gaussian noise at different input SNR to 100 number dataset of MITDB ECG signal. (c) Mean PRD of conventional filtering, adaptive filtering, wavelet denoising, NLM, EMD, proposed methodology (EMD + NLM) for cancelation of added white Gaussian noise at different input SNR to 100 number dataset of MITDB ECG signal.

676 677 678 679 680 681

information related to heart can be kept by the proposed denoising method. After denoising of the ECG signal, the P wave, T wave, and QRS complex are clearly visible, so different diseases like atrial fibrillation, increase chance of sudden cardiac death, arrhythmia, and different cardiovascular diseases can be identified.

5.

Conclusion

In this paper, empirical mode decomposition with non-local mean technique, by using differential standard deviation is used to remove the noise and preserves the edges of the ECG signal. The mean square error, percent root mean square

Please cite this article in press as: Kumar S, et al. Denoising of Electrocardiogram (ECG) signal by using empirical mode decomposition (EMD) with non-local mean (NLM) techniqueQ1. Biocybern Biomed Eng (2018), https://doi.org/10.1016/j.bbe.2018.01.005

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Fig. 14 – (a) SNR improvement of conventional filtering, adaptive filtering, wavelet denoising, NLM, EMD, proposed methodology (EMD + NLM) for cancelation of added white Gaussian noise at S5 dB SNR to different ECG signals. (b) MSE of conventional filtering, adaptive filtering, wavelet denoising, NLM, EMD, proposed methodology (EMD + NLM) for cancelation of added white Gaussian noise at S5 dB SNR to different ECG signals. (c) PRD of conventional filtering, adaptive filtering, wavelet denoising, NLM, EMD, proposed methodology (EMD + NLM) for cancelation of added white Gaussian noise at S5 dB SNR to different ECG signals.

Please cite this article in press as: Kumar S, et al. Denoising of Electrocardiogram (ECG) signal by using empirical mode decomposition (EMD) with non-local mean (NLM) techniqueQ1. Biocybern Biomed Eng (2018), https://doi.org/10.1016/j.bbe.2018.01.005

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difference, and SNR improvement of the proposed methodology (empirical mode decomposition with non-local mean technique) is calculated at different SNR by addition of colored, Gaussian and white noise to the first channel of seven datasets (215, 115, 106, 105, 104, 103, 100) from the MIT-BIH arrhythmia database. The proposed methodology shows lesser mean square error and percent root mean square difference, and better SNR improvement and preservation of edges compared to other existing techniques like conventional filtering, adaptive filtering, wavelet denoising technique, non-local mean technique, empirical mode decomposition technique for removal of added colored Gaussian noise and white Gaussian noise to the ECG signal.

701

Financial disclosure

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The authors certify they have no affiliations with or involvement in any organization or entity with any financial or nonfinancial interest in the subject matter or materials discussed in this manuscript.

706

Conflict of interest

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The authors declare that they have no conflict of interest.

708

Ethical approval

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This article does not contain any studies with human participants or animals performed by any of the authors.

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Acknowledgement

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Author would like to thank editor and reviewers of the manuscript for valuable suggestion to improve the manuscript.

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Please cite this article in press as: Kumar S, et al. Denoising of Electrocardiogram (ECG) signal by using empirical mode decomposition (EMD) with non-local mean (NLM) techniqueQ1. Biocybern Biomed Eng (2018), https://doi.org/10.1016/j.bbe.2018.01.005

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Please cite this article in press as: Kumar S, et al. Denoising of Electrocardiogram (ECG) signal by using empirical mode decomposition (EMD) with non-local mean (NLM) techniqueQ1. Biocybern Biomed Eng (2018), https://doi.org/10.1016/j.bbe.2018.01.005