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    • V.Supraja, S.Safiya / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 3, Issue 2, March -April 2013, pp.253-257 ECG De-Noising using thresholding based on Wavelet transforms V.Supraja*, S.Safiya** *, ** Assistant Professor, Department of Electronics and Communication Engineering, Ravindra college of engineering for women, Kurnool-518002, A.P., India.Abstract The electrocardiogram (ECG) is widely line wandering, a low frequency component is dueused for diagnosis of heart diseases. Good quality to the rhythmic inhalation and exhalation duringof ECG is utilized by physicians for respiration. J. Pan et al. showed that the QRSinterpretation and identification of physiological complex power spectrum density (PSD) –(5-15 Hz)and pathological phenomena. However, in real overlaps with the muscle noise [1], while P and Tsituations, ECG recordings are often corrupted waves PSD overlaps with respiration action andby artifacts. Noise severely limits the utility of the blood pressure at low frequency band (usually fromrecorded ECG and thus need to be removed, for 0.1 to 1 Hz)[2]. Furthermore, the non-stationarybetter clinical evaluation. Donoho and Johnstone behavior of the ECG signal, that becomes severe in[4, 5, 10] proposed wavelet thresholding de- the cardiac anomaly case [3], incites researchers tonoising method based on discrete wavelet analyze the ECG signal. Wavelet thresholding de-transform (DWT) with universal threshold is noising method based on discrete wavelet transformsuitable for non-stationary signals such as ECG (DWT) proposed by Donoho et al. is often used insignal. In the present paper a new thresholding de-noising of ECG signal [4, 5]. In 1999, Agantetechnique is proposed for de-noising of ECG used it in de-noising of ECG signal [6].signal. This new de-noising method is called asimproved thresholding de-noising method could Wavelet thresholding de-noising methodsbe regarded as a compromising between hard- deals with wavelet coefficients using a suitableand soft-thresholding de-noising methods. The chosen threshold value in advance. The waveletproposed method selects the best suitable wavelet coefficients at different scales could be obtained byfunction based on DWT at the decomposition taking DWT of the noisy signal. Normally, thoselevel of 5, using mean square error (MSE) and wavelet coefficients with smaller magnitudes thanoutput SNR. The advantage of the improved the preset threshold are caused by the noise and arethresholding de-noising method is that it retains replaced by zero, and the others with largerboth the geometrical characteristics of the magnitudes than the preset threshold are caused byoriginal ECG signal and variations in the original signal mainly and kept (hard-thresholdingamplitudes of various ECG waveforms case) or shrunk (the soft-thresholding case). Theneffectively. The experimental results indicate that the de-noised signal could be reconstructed fromthe proposed method is better than traditional the resulting wavelet coefficients. These methodswavelet thresholding de-noising methods in the are simple and easy to be used in de-noising ofaspects of remaining geometrical characteristics ECG signal. But hard-thresholding de-noisingof ECG signal and in improvement of signal-to- method may lead to the oscillation of thenoise ratio (SNR). reconstructed ECG signal and the soft-thresholding de-noising method may reduce the amplitudes ofKeywords: ECG signal, wavelet de-noising, ECG waveforms, and especially reduce thediscrete wavelet transform, improved thresholding. amplitudes of the R waves. To overcome the above said disadvantages an improved thresholding de-1. Introduction noising method is proposed [13, 14, 15, and 16]. Electrocardiogram (ECG) signal, theelectrical interpretation of the cardiac muscle 2. Methodsactivity, is very easy to interfere with different ECG signal is easy to be contaminated bynoises while gathering and recording. The most random noises uncorrelated with the ECG signal,troublesome noise sources are the Electromyogram such as EMG, baseline wandering and so on, which(EMG) signal, instability of electrode-skin effect, 50 can be approximated by a white Gaussian noise/ 60 Hz power line interference and the baseline source [6, 7].wandering. Such noises are difficult to remove The method can be divided into the following steps:using typical filtering procedures. The EMG, a high Noise Generation and addition: A random noise isfrequency component, is due to the random generated and added to the original signal. So, thecontraction of muscles, while the abrupt transients noisy ECG signal can be assumed with finite lengthare due to sudden movement of the body. The base as follows: 253 | P a g e
    • V.Supraja, S.Safiya / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 3, Issue 2, March -April 2013, pp.253-257y (n) = x (n) + d (n) , n = 1,2, . . ., N. where   1 and   R . Because the magnitudes of(1) the wavelet coefficients related to the Gauss white noise decreases as the scale j increases, hence thewhere x (n) is the clean original MIT-BIH ECG threshold value will be chosen asdata signal with DC component rejected, d (n) isGaussian white noise with zero mean and constant Tj   2log d j / log( j  1) (6)variance, y(n) is the noisy ECG signal. For each level, find the threshold value that gives the minimum error between the detailed coefficients1. Decomposing of the noisy signals using of the noisy signal and those of original signal.wavelet From equation (5), the improved wavelettransform: thresholding de-noising method has the following characters:Using the discrete wavelet transform by selecting Assured the continuity of estimated waveletmother wavelet, the noisy signal is decomposed, at coefficients d j at position  T j , so that thethe decomposition level of 5. As a result oscillation of the reconstructed ECG signal isapproximate coefficients a j and detail coefficients avoided.d j are obtained.  Once  is fixed the deviations between d j and d j2. Apply thresholding, to obtain the estimated decrease with the increase of the absolute values of  d j , when d j  T j , if equation (5) satisfies :wavelet coefficients d j .  lim d j  d j (7)For each level a threshold value is found, and it is d j applied for the detailed coefficients d j . It makes the reconstructed ECG signal remain the characteristics of the original ECG signal and keep(a) Hard-thresholding method: the amplitudes of R waves effectively. Equation (5) will be equivalent to hard-thresholding d j , d j Tj when    and will be equivalent to soft- dj  (2) thresholding, when   1 . This shows that the 0,  d j Tj improved threshold de-noising method can bewhere preset threshold is T j   2log d j adapted to both hard- and soft-thresholding de- noising methods. Therefore, the improved(3) thresholding de-noising method could be regardedThe  can be estimated by the wavelet coefficients as a compromise between the hard- and soft- with σ = median d j   / 0.6745 . Here median ( thresholding de-noising methods. So, that the improved thresholding de-nosing method presented d j ) denotes the median value of the absolute in this paper could choose an appropriate  by trail –and-error to satisfy the request of de-noising of thevalues of wavelet coefficients d j . ECG signal. 3. Reconstructing the de-noised ECG signal x ( n) Evaluation Criteria: We utilize both the mean  square error (MSE) value and SNRo value between from d j and a j by inverse discrete wavelet the constructed de-noised ECG signal x(n) and thetransform (IDWT). original ECG signal with DC offset rejected x(n) (the reference ECG signal to evaluate our method).The same steps are to be followed for softthresholding, and improved thresholding de-noising Determination of Mean square error: For ECGmethods. signal de-noising, the best suitable wavelet functionb) Soft-thresholding method: is achieved based on the mean square error (MSE)  sgn(d j )( d j  T ), d j  T j value between the de-noised ECG signal x(n) and   dj  (4) the original with DC component rejected signal 0,  d j  Tj x ( n) . 1 N (c) Improved thresholding method: MSE (w, l )   ( x(i)  x(i))2 N i 1 (8) sgn(d )( d   Tj  d j .T ), d  T   where w is the wavelet function, l is the level ofdj  j j j j j (5) wavelet de-noising and N is the length of the ECG 0,  d j  Tj segment[17]. 254 | P a g e
    • V.Supraja, S.Safiya / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 3, Issue 2, March -April 2013, pp.253-257 (coefficients). Therefore, high quality denoisedDetermination of SNR Criteria: The output SNR signal can be accomplished. Our study establishesis given by particular approach to fit ECG signal that has N nonstationary clinical information. To preserve the x i 1 2 (i ) distinct ECG waves and different low passSNRo = 10 log ( N  ) (9) frequency shapes, the method thresholds detailed  ( x(i)  x(i)) 2 wavelet coefficients only. i 1 This concept is used to return the low frequenciesSNRo values to determine the wavelet function for (P-wave where the frequency is less than 8Hz andde-noising ECG signal [17]. T-wave where the frequency is less than 11Hz) by inverse discrete wavelet transform (IDWT).3. Results and analysis Donohos method deforms, slightly, low frequency P and T-waves, by creating small wave at theTo validate the superiority of the proposed beginning of these waves.improved thresholding de-noising method, ECG Comparative Analysis:signal in MIT-BIH database is intercepted to be the The comparative analysis was carried out on theoriginal ECG signal. The length of the original ECG ECG data record with SNR = -10 of the referencesignal (i.e., the number of the sample points) is ECG signal and  -value at 21 in the improvedN=1024 (see Fig 1(a)). Gauss white noise is added thresholding de-noising method. The table.1to the original ECG signal, the noisy ECG signal is summarizes the obtained output MSE and SNRshown in Fig 1(b). Noise reduction Procedures were values for hard-, soft-, and improved thresholdingimplemented in Mat lab 7.0.1. The effectiveness of de-noising methods respectively. This will ensurede-noising process for 14 wavelet functions are the performance superiority of improvedtested [18]: Daubechies proposed functions [5] (db2, thresholding de-noising method algorithm overdb3, db4, db5, db6, db7, db8), and their hard- and soft- thresholding methods. The db5 andmodifications so-called Symlets wavelets (sym2, sym8 are showing better suitable wavelets for de-sym3, sym4, sym5, sym6, sym7, sym8), at the noising of ECG signal.decomposed scale of 5. The DWT wavelet de-noising is performed for hard-thresholding, soft- 4. Conclusionthresholding and improved thresholding de-noising The wavelets transform allows processing of non-methods respectively to de-noise the noisy ECG stationary signals such as ECG signal. The proposedsignal. method shows a new experimental threshold valueIn improved thresholding de-noising method with for each decomposition level of wavelet coefficientsDWT, the coefficient  is chosen as  =21. The fig.1(c)-(e) shows that the de-noised the ECG signals of d j . This threshold value is accomplished at by using the hard-, soft- and improved-thresholding =21 providing better MSE and SNR valuesde-noising methods respectively. From fig. 1(c), it comparative to hard- and soft- thresholdingcan see that hard– thresholding using DWT is better methods. In this study, it shows that proposedin remaining the characteristics of original ECG improved thresholding de-noising method in thissignal and the loss of the amplitudes of R waves is paper is superior to other traditional thresholdingnot obvious. It is seen from fig.1(d) soft- de-noising methods in many aspects such asthresholding de-noising using DWT gainsgood smoothness, remaining the geometricalsmoothness but the amplitude of R waves in characteristics of the original ECG signal with DCreconstructed ECG signal is reduced obviously. offset rejected. Though, the  value has taken at 21From fig 1(e), the improved thresholding de-noising based on the maximum SNR value using trial andmethod via DWT can not only remain the error method. So, it is valuable to study further togeometrical characteristics of original ECG signal find appropriate  value exactly. On other hand, toand gain good smoothness, but also keep the develop more appropriate and effective thresholdingamplitudes of R waves in reconstructed ECG signal representation is also a valuable problem to studyefficiently. further.The proposed method is based on choosingthreshold value by finding minimum error ofdenoised signal and original wavelet subsignal 255 | P a g e
    • V.Supraja, S.Safiya / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 3, Issue 2, March -April 2013, pp.253-257 Fig.1 De-noising of ECG signal using threshold methods with Sym8Table 1: MSE and SNR values for the de-noising methods using Daubechies wavelets and Symlet wavelets Daubechies wavelets Symlet wavelets Denoising Denoising Wavelet MSE SNRo Wavelet MSE SNRo method method Hard 10.0379 14.4833 Hard 10.3987 14.2894 db2 Soft 9.1424 14.8544 sym2 Soft 9.6900 14.5527 Improved 8.1042 15.1877 Improved 7.3250 15.6014 Hard 10.0257 14.4590 Hard 9.7569 14.5024 db3 Soft 9.2329 14.7818 sym3 Soft 9.0883 14.7639 Improved 6.7172 15.9901 Improved 6.4657 16.0977 Hard 10.1304 14.4104 Hard 10.2239 14.3775 db4 Soft 9.3490 14.7232 sym4 Soft 9.4295 14.6844 Improved 6.4488 16.1768 Improved 6.2522 16.3072 Hard 9.7859 14.5275 Hard 10.0501 14.4386 db5 Soft 8.8397 14.9290 sym5 Soft 9.3407 14.6972 Improved 5.6444 16.7279 Improved 6.4077 16.1811 Hard 10.1955 14.3753 Hard 10.1919 14.3517 db6 Soft 9.3151 14.7343 sym6 Soft 9.3550 14.6959 Improved 6.5840 16.0738 Improved 6.3105 16.2333 Hard 9.8823 14.4861 Hard 10.0422 14.3989 db7 Soft 9.0764 14.8007 sym7 Soft 9.1510 14.7601 Improved 6.4528 16.1318 Improved 6.3309 16.1981 Hard 10.1248 14.3846 Hard 10.1374 14.3713 db8 Soft 9.3411 14.6935 sym8 Soft 9.4309 14.6522 Improved 6.5094 16.1057 Improved 6.2854 16.2472 256 | P a g e
    • V.Supraja, S.Safiya / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 3, Issue 2, March -April 2013, pp.253-257References [12] R.R. Coifman and D.L. Donoho. [1] Pan. J and W.J. Tompkins, “A real-time “Translation-invariant de-noising”, in QRS detection algorithm”, IEEE Trans. Wavelets and Statistics, Springer Lecture Bio-Med. Eng., 31:715-717, 1985. Notes in Statistics 103, Newyork: Springer-Verlag, pp.125-150, 1994. [2] P.V.E. Mc Clintock, and A. Stefanovska, “Noise and deterministic in cardiovascular [13] T.D. Bui and G. Chen, “Translation- dynamics”, Physica A., 314: 69-76, 2002. invariant de-noising using multi-wavelets”, IEEE Trans. Signal Processing, vol.46, pp. [3] M. Sivannarayana, and D.C. Reddy, 3414-3420, 1998. “Biorthogonal wavelet transform for ECG parameters estimation”, Med. Eng. and [14] S.A. Chouakri, and F. Bereksi-Reguig, Physics, ELSEVIER, 21:167-174, 1999. “Wavelet denoising of the electrocardiogram signal based on the [4] D.L. Donoho and I.M. Johnstone, “Ideal corrupted noise estimation”, Computers in spatial adaptation via wavelet shrinkage”, Cardiology, Vol.32, pp.1021-1024, 2005. Biometrika, 1994, Vol.81, pp. 425-455. [15] S.A. Chouakri, F. Bereksi-Reguig, S. [5] D.L. Donoho, “De-noising by soft Ahmaidi, and O.Fokapu, “ECG signal thresholding”, IEEE Trans. Trans. smoothing based on combining wavelet Inform. Theory, vol. 41, pp. 613-627, denoising levels”, Asian Journal of 1995. Information Technology, Vol. 5(6), pp. 666-627, 2006. [6] P.M. Agante and J.P. Marques de sa, “ECG noise filtering using wavelets with soft- [16] Mikhled Alfaouri and Khaled Daqrouq, thresholding methods”, Computers in “ECG signal denoising by wavelet Cardiology, vol. 26, pp. 523-538, 1999. transform thresholding,” American journal of Applied Sciences, vol. 5(3), pp.276-281, [7] F.N. Ucar, M. Korurek, and E. Yazgan, “A 2008. noise reduction algorithm in ECG signals using wavelet transforms’, Biomedical [17] M.Kania, M.Fereniec, and R. Maniewski, Engineering Days, Proceedings of the 1998 “Wavelet denoising for multi-lead high 2nd International Conference, pp.36- resolution ECG signals”, Measurement 38,1998. Science review, vol.7.pp. 30-33, 2007. [8] ftp://ftp.ieee.org/uploads/press/rangayyan/ V.Supraja received B.Tech degree in Electronics S. Mallat, “A theory for multiresolution and Communication Engineering from Sreenidhi signal decomposition: the wavelet Institute of Technology and M.Tech degree in representation”, IEEE Pattern Anal. and Electronic Instrumentation & Communication Machine Intel., vol. 11, no. 7, pp. 674-693, systems from Sri Venkateswara University college 1989. of Engineering, Tirupati in 2007 and 2010, respectively. At present, she is working as Assistant [9] D.L. Donoho, and I.M. Johnstone, Professor, Department of Electronics and “Adapting to unknown smoothness via Communication Engineering, Ravindra college of wavelet shrinkage”, J. ASA, vol. 90, pp. engineering for women, Kurnool, Andhra Pradesh, 1200–1223, 1995. India. [10] G. Song and R. Zhao, “Three novel models S.Safiya received B.Tech degree in Electronics and of threshold estimator for wavelets Communication Engineering from B.V.C and coefficients”, 2nd International Conference M.Tech degree in Embedded systems from Bharat on Wavelet Analysis and Its Applications, Institute of Technology in 2006 and 2011, Berlin: Springer-verlag, pp.145-150, 2001. respectively. At present, she is working as Assistant Professor, Department of Electronics and [11] W. Gao, H. Li, Z. Zhuang, and T. Wang, Communication Engineering, Ravindra college of “De-noising of ECG signal based on engineering for women, Kurnool, Andhra Pradesh, stationary wavelet transform”, Acta India. Electronica Sinica, vol.32, pp.238-240, 2003. 257 | P a g e