Abstract
Introduction
The analysis of electrocardiogram (ECG) signals allows the experts to diagnosis several cardiac disorders. However, the accuracy of such diagnostic depends on the signals quality. In this paper it is proposed a simple method for powerline interference (PLI) removal based on the wavelet decomposition, without the use of thresholding techniques.
Methods
This method consists in identifying the ECG and noise frequency range for further zeroing wavelet detail coefficients in the subbands with no ECG coefficients in the frequency content. Afterward, the enhanced ECG signal is obtained by the inverse discrete wavelet transform (IDWT). In order to choose the wavelet function, several experiments were performed with synthetic signals with worse SignaltoNoise Ratio (SNR).
Results
Considering the relative error metrics and runtime, the best wavelet function for denoising was Symlet 8. Twenty synthetic ECG signals with different features and eight real ECG signals, obtained in the Physionet Challenge 2011, were used in the experiments. Results show the advantage of the proposed method against thresholding and notch filter techniques, considering classical metrics of assessment. The proposed method performed better for 75% of the synthetic signals and for 100% of the real signals considering most of the evaluation measures, when compared with a thresholding technique. In comparison with the notch filter, the proposed method is better for all signals.
Conclusion
The proposed method can be used for PLI removal in ECG signals with superior performance than thresholding and notch filter techniques. Also, it can be applied for high frequencies denoising even without a priori frequencies knowledge.
Keywords
Powerline interference; Denoising ECG signals; Wavelet decomposition
Introduction
ECG signals represent the heart electrical activity and they are obtained through electrodes placed in specific regions of the human body. There are five main waves characterizing ECG signals: P, Q, R, S, and T. Each wave or complex has an exclusive significance. The combination of Q, R and S waves forms which is known as QRS complex. The P wave and the QRS complex represent the atrial and ventricular depolarization, respectively. On the other hand, the T wave characterizes the ventricular repolarization. The spectrum of the QRS complex is located in the ECG frequency bands whose typical frequency components range from 10 Hz to 25 Hz ( Köhler et al., 2002 Köhler BU, Hennig C, Orglmeister R. The principles of software QRS detection. IEEE Eng Med Biol Mag. 2002; 21(1):4257. http://dx.doi.org/10.1109/51.993193. PMid:11935987.
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) and its detection is still subject of many studies. Pan and Tompkins (1985) Pan J, Tompkins WJ. A realtime QRS detection algorithm. IEEE Trans Biomed Eng. 1985; 32(3):2306. http://dx.doi.org/10.1109/TBME.1985.325532. PMid:3997178.
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developed an objective QRS detection algorithm using a bandpass filter from 5 Hz to 12 Hz. Zidelmal et al. (2012) Zidelmal Z, Amirou A, Adnane M, Belouchrani A. QRS detection based on wavelet coefficients. Comput Methods Programs Biomed. 2012; 107(3):4906. http://dx.doi.org/10.1016/j.cmpb.2011.12.004. PMid:22296976.
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computed the power spectrum for four QRS types concluding that their energies are concentrated in the range from 5 Hz to 22 Hz. Such spectral information is used to QRS complexes detection in Challenge 2011 (Training Set A) database ( Oliveira et al., 2015 Oliveira BR, Duarte MAQ, Vieira Filho J. Detecção de complexos QRS do ECG pela decomposição em valores singulares em multirresolução. In: Anais da IX ENAMA; 2015 Nov 46; Cascavel, Brasil; São Carlos: SBMAC; 2015. p. 1434. ). In addition, it is important to remark that ECG signals are nonstationary, nonsymmetric in relation to the
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).
The specific morphology of the ECG signals allows identifying various cardiac diseases. However, for an accurate analysis, signals should have high SignaltoNoise Ratio (SNR) ( Łęski and Henzel, 2005 Łęski JM, Henzel N. ECG baseline wander and powerline interference reduction using nonlinear filter bank. Signal Process. 2005; 85(4):78193. http://dx.doi.org/10.1016/j.sigpro.2004.12.001.
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). Low SNR can difficult the analysis performed by experts or computational applications, since it changes the signal waveform. Typical noise present in ECG signals are due to powerline interference in a frequency band varying from 50 Hz to 60 Hz ( Łęski and Henzel, 2005 Łęski JM, Henzel N. ECG baseline wander and powerline interference reduction using nonlinear filter bank. Signal Process. 2005; 85(4):78193. http://dx.doi.org/10.1016/j.sigpro.2004.12.001.
http://dx.doi.org/10.1016/j.sigpro.2004...
; Patil and Chavan, 2012 Patil PB, Chavan MS. A wavelet based method for denoising of biomedical signal. In: Proceedings of International Conference on Pattern Recognition, Informatics and Medical Engineering (PRIME); 2012 Mar 2123; Salem, Tamilnadu, India. New Jersey: IEEE; 2012. p. 27883. http://dx.doi.org/10.1109/ICPRIME.2012.6208358.
http://dx.doi.org/10.1109/ICPRIME.2012....
; Rahman et al., 2010 Rahman MZU, Shaik RA, Reddy DVRK. Baseline wander and power line interference elimination from cardiac signals using error nonlinearity LMS algorithm. In: International Conference on Systems in Medicine and Biology (ICSMB). 2010 Dec 1618; Kharagpur, India; New Jersey: IEEE; 2010. p. 21720. ) depending on the country. It occurs due to interferences of electrical equipment as Xray, air conditioners, elevators ( Patil and Chavan, 2012 Patil PB, Chavan MS. A wavelet based method for denoising of biomedical signal. In: Proceedings of International Conference on Pattern Recognition, Informatics and Medical Engineering (PRIME); 2012 Mar 2123; Salem, Tamilnadu, India. New Jersey: IEEE; 2012. p. 27883. http://dx.doi.org/10.1109/ICPRIME.2012.6208358.
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), and also due to the differences in electrode impedances ( Bahoura and Ezzaidi, 2010 Bahoura M, Ezzaidi H. FPGAimplementation of waveletbased denoising technique to remove powerline interference from ECG signal. Inf Technol Appl Biomed (ITAB). In: Proceedings of the 10th IEEE International Conference; 2010 Nov 35; Corfu, Greece. New Jersey: IEEE; 2010. p. 14. ).
Several researchers have proposed denoising approaches to enhance ECG signals and preserve their original characteristics. Some noise reduction techniques are based on digital filters, wavelet transform and adaptive filtering ( AlMahamdy and Riley, 2014 AlMahamdy M, Riley HB. Performance study of different denoising methods for ECG signals. Procedia Comput Sci. 2014; 37:32532. http://dx.doi.org/10.1016/j.procs.2014.08.048.
http://dx.doi.org/10.1016/j.procs.2014....
); singular value decomposition ( Bandarabadi and KaramiMollaei, 2010 Bandarabadi AAJGM, KaramiMollaei MR. ECG denoising using singular value decomposition. Aust J Basic Appl Sci. 2010; 4(7):210913. ); independent component analysis ( Phegade and Mukherji, 2013 Phegade M, Mukherji P. ICA based ECG signal denoising. In: Proceedings of the International Conference on Advances in Computing, Communications and Informatics (ICACCI); 2013 Aug 2225; Mysore, India; New Jersey: IEEE; 2013. p. 167580. ) and Stransform ( Das and Ari, 2013 Das M, Ari S. Analysis of ECG signal denoising method based on stransform. IRBM. 2013; 34(6):36270. http://dx.doi.org/10.1016/j.irbm.2013.07.012.
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). Among the algorithms for PLI removal there are digital processing methods based on: fuzzy thresholding ( Üstündağ et al., 2012 Üstündağ M, Gökbulut M, Sengür A, Ata F. Denoising of weak ECG signals by using wavelet analysis and fuzzy thresholding. Netw Model Anal Health Inform Bioinform. 2012; 1(4):13540. http://dx.doi.org/10.1007/s1372101200155.
http://dx.doi.org/10.1007/s1372101200...
); nonlinear filter bank ( Łęski and Henzel, 2005 Łęski JM, Henzel N. ECG baseline wander and powerline interference reduction using nonlinear filter bank. Signal Process. 2005; 85(4):78193. http://dx.doi.org/10.1016/j.sigpro.2004.12.001.
http://dx.doi.org/10.1016/j.sigpro.2004...
); Fast Fourier Transform and adaptive nonlinear noise estimator ( Shirbani and Setarehdan, 2013 Shirbani F, Setarehdan SK. ECG power line interference removal using combination of FFT and adaptive nonlinear noise estimator. In: Proceedings of the 21st Iranian Conference on Electrical Engineering (ICEE). 2013 May 1416. Mashhad, Iran. New Jersey: IEEE; 2013. p. 15. http://dx.doi.org/10.1109/IranianCEE.2013.6599622.
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); Empirical Mode Decomposition ( Agrawal and Gupta, 2013 Agrawal S, Gupta A. Fractal and EMD based removal of baseline wander and powerline interference from ECG signals. Comput Biol Med. 2013; 43(11):188999. http://dx.doi.org/10.1016/j.compbiomed.2013.07.030. PMid:24209934.
http://dx.doi.org/10.1016/j.compbiomed....
); neural networks ( Mateo et al., 2008 Mateo J, Sanchez C, Tortes A, Cervigon R, Rieta JJ. Neural network based canceller for powerline interference in ECG signals. In: Proceedings of the 35th Annual Computers in Cardiology Conference (CinC); 2008 Sep 1417; Bolongna, Italy. New Jersey: IEEE; 2008. p. 107376. http://dx.doi.org/10.1109/CIC.2008.4749231.
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) and wavelet transform ( Agrawal and Gupta, 2013 Agrawal S, Gupta A. Fractal and EMD based removal of baseline wander and powerline interference from ECG signals. Comput Biol Med. 2013; 43(11):188999. http://dx.doi.org/10.1016/j.compbiomed.2013.07.030. PMid:24209934.
http://dx.doi.org/10.1016/j.compbiomed....
; Garg et al., 2011 Garg G, Gupta S, Singh V, Gupta JRP, Mittal AP. Identification of optimal waveletbased algorithm for removal of power line interferences in ECG signals. In: Proceedings of the India International Conference on Power Electronics; 2011 Jan 2830; New Delhi, India. New Jersey: IEEE; 2011. p. 15. http://dx.doi.org/10.1109/IICPE.2011.5728090.
http://dx.doi.org/10.1109/IICPE.2011.57...
; Poornachandra and Kumaravel, 2008 Poornachandra S, Kumaravel N. A novel method for the elimination of power line frequency in ECG signal using hyper shrinkage function. Digit Signal Process. 2008; 18(2):11626. http://dx.doi.org/10.1016/j.dsp.2007.03.011.
http://dx.doi.org/10.1016/j.dsp.2007.03...
; Rahman et al., 2010 Rahman MZU, Shaik RA, Reddy DVRK. Baseline wander and power line interference elimination from cardiac signals using error nonlinearity LMS algorithm. In: International Conference on Systems in Medicine and Biology (ICSMB). 2010 Dec 1618; Kharagpur, India; New Jersey: IEEE; 2010. p. 21720. ).
Wavelet analysis has been successfully used for ECG signal denoising because it deals well with nonstationary signals and also presents better resolution in timefrequency domain than Fourier analysis ( Rahman et al., 2010 Rahman MZU, Shaik RA, Reddy DVRK. Baseline wander and power line interference elimination from cardiac signals using error nonlinearity LMS algorithm. In: International Conference on Systems in Medicine and Biology (ICSMB). 2010 Dec 1618; Kharagpur, India; New Jersey: IEEE; 2010. p. 21720. ). In the comparative study presented by AlMahamdy and Riley (2014) AlMahamdy M, Riley HB. Performance study of different denoising methods for ECG signals. Procedia Comput Sci. 2014; 37:32532. http://dx.doi.org/10.1016/j.procs.2014.08.048.
http://dx.doi.org/10.1016/j.procs.2014....
, the wavelet transform produced better results in most of the experiments. Chouakri et al. (2006) Chouakri SAS, BereksiReguig AF, Fokapu O. ECG signal smoothing based on combining wavelet denoising levels. Asian J Inf Technol. 2006; 5(6):66677. compared the performance of Butterworth filters and the multilevel wavelet transform, concluding that improved results were achieved by the wavelet technique. Usually, waveletbased methods for ECG denoising use thresholding techniques with some additional processing ( Agante and Sa, 1999 Agante PM, Sa JPM. ECG noise filtering using wavelets with softthresholding methods. Comput Cardiol. 1999; 26:5358. ; AlMahamdy and Riley, 2014 AlMahamdy M, Riley HB. Performance study of different denoising methods for ECG signals. Procedia Comput Sci. 2014; 37:32532. http://dx.doi.org/10.1016/j.procs.2014.08.048.
http://dx.doi.org/10.1016/j.procs.2014....
; Awal et al., 2014 Awal MA, Mostafa SS, Ahmad M, Rashid MA. An adaptive level dependent wavelet thresholding for ECG denoising. Biocybern Biol Eng. 2014; 34(4):23849. ; Bahoura and Ezzaidi, 2010 Bahoura M, Ezzaidi H. FPGAimplementation of waveletbased denoising technique to remove powerline interference from ECG signal. Inf Technol Appl Biomed (ITAB). In: Proceedings of the 10th IEEE International Conference; 2010 Nov 35; Corfu, Greece. New Jersey: IEEE; 2010. p. 14. ; Chouakri et al., 2006 Chouakri SAS, BereksiReguig AF, Fokapu O. ECG signal smoothing based on combining wavelet denoising levels. Asian J Inf Technol. 2006; 5(6):66677. ; Garg et al., 2011 Garg G, Gupta S, Singh V, Gupta JRP, Mittal AP. Identification of optimal waveletbased algorithm for removal of power line interferences in ECG signals. In: Proceedings of the India International Conference on Power Electronics; 2011 Jan 2830; New Delhi, India. New Jersey: IEEE; 2011. p. 15. http://dx.doi.org/10.1109/IICPE.2011.5728090.
http://dx.doi.org/10.1109/IICPE.2011.57...
; GermánSalló, 2010 GermánSalló Z. Nonlinear filtering in ECG signal denoising. Acta Univ Sapientiae Elec Mech Eng. 2010; 2:13645. ; Karthikeyan et al., 2012 Karthikeyan P, Murugappan M, Yaacob S. ECG signal denoising using wavelet thresholding techniques in human stress assessment. Int J Elec Eng Inf. 2012; 4(2):306. ; Li et al., 2009 Li S, Liu G, Lin Z. Comparisons of wavelet packet, lifting wavelet and stationary wavelet transform for denoising ECG. In: Proceedings of the 2nd IEEE International Conference on Computer Science and Information Technology (ICCSIT 2009); 2009 Aug 811; Beijing, China; New Jersey: IEEE; 2009. p. 4914. ; Patil and Chavan, 2012 Patil PB, Chavan MS. A wavelet based method for denoising of biomedical signal. In: Proceedings of International Conference on Pattern Recognition, Informatics and Medical Engineering (PRIME); 2012 Mar 2123; Salem, Tamilnadu, India. New Jersey: IEEE; 2012. p. 27883. http://dx.doi.org/10.1109/ICPRIME.2012.6208358.
http://dx.doi.org/10.1109/ICPRIME.2012....
; Poornachandra and Kumaravel, 2008 Poornachandra S, Kumaravel N. A novel method for the elimination of power line frequency in ECG signal using hyper shrinkage function. Digit Signal Process. 2008; 18(2):11626. http://dx.doi.org/10.1016/j.dsp.2007.03.011.
http://dx.doi.org/10.1016/j.dsp.2007.03...
; Üstündağ et al., 2012 Üstündağ M, Gökbulut M, Sengür A, Ata F. Denoising of weak ECG signals by using wavelet analysis and fuzzy thresholding. Netw Model Anal Health Inform Bioinform. 2012; 1(4):13540. http://dx.doi.org/10.1007/s1372101200155.
http://dx.doi.org/10.1007/s1372101200...
). Patil and Chavan (2012) Patil PB, Chavan MS. A wavelet based method for denoising of biomedical signal. In: Proceedings of International Conference on Pattern Recognition, Informatics and Medical Engineering (PRIME); 2012 Mar 2123; Salem, Tamilnadu, India. New Jersey: IEEE; 2012. p. 27883. http://dx.doi.org/10.1109/ICPRIME.2012.6208358.
http://dx.doi.org/10.1109/ICPRIME.2012....
compared the PLI removal for different wavelet basis using hard and soft shrinkage functions. They conclude that hard thresholding achieves better SNR scores than soft thresholding, and the best wavelet basis depends on the analyzed signal.
Garg et al. (2011) Garg G, Gupta S, Singh V, Gupta JRP, Mittal AP. Identification of optimal waveletbased algorithm for removal of power line interferences in ECG signals. In: Proceedings of the India International Conference on Power Electronics; 2011 Jan 2830; New Delhi, India. New Jersey: IEEE; 2011. p. 15. http://dx.doi.org/10.1109/IICPE.2011.5728090.
http://dx.doi.org/10.1109/IICPE.2011.57...
worked on optimal waveletbased algorithm for ECG denoising, analyzing SNR for several wavelet families, decomposition level and threshold selection method. In order to calculate the threshold, four rules were used: minmax, rigorous sure, universal and heuristic sure. The best configuration was achieved with the Symlet wavelet with ten vanishing moments and five decomposition levels, hard shrinkage function and heuristic sure rule or rigorous sure thresholding. Poornachandra and Kumaravel (2008) Poornachandra S, Kumaravel N. A novel method for the elimination of power line frequency in ECG signal using hyper shrinkage function. Digit Signal Process. 2008; 18(2):11626. http://dx.doi.org/10.1016/j.dsp.2007.03.011.
http://dx.doi.org/10.1016/j.dsp.2007.03...
proposed to use of hyper shrinkage function in the subbands that contained the PLI noise at some decomposition level. The obtained results were better when compared to those of the stateoftheart algorithms.
In this paper, it is proposed to use discrete wavelet transform (DWT) to decompose an ECG signal degraded by high powerline interference. The goal is to have the ECG signal represented by the approximation coefficients and the noise by the detail coefficients. The basic idea is to inspect the ECG and noise frequency range in each subband of the wavelet filter bank. The wavelet scale whose frequency range exceeds the maximum frequency of the ECG signals is set to zero. Then, the IDWT is applied in order to obtain a better quality signal without the use of thresholding techniques. It is common that such techniques do not completely eliminate noise, generating residual noise that can still distorts the QRS waveform. Therefore, this original ECG analysis methodology eliminates the need of thresholding function and is based solely on wavelet filter bank and the characteristics of PLI. Comparisons with a thresholding technique and a classical digital filter were carried out to demonstrate the effectiveness of the proposed method. Furthermore, the proposed method presents low computational load, reduces the residual noise and can be easily implemented.
Methods
A noisy ECG,
where
Dynamical model for generating synthetic ECG signals
In order to analyze ECG denoising algorithms performances, many metrics based on comparisons between the estimated signal and the original one have been proposed. Real ECG signals may have other noise besides PLI. To focus only on this kind of noise, synthetic ECG signals are used in some experiments. The mathematical model for generating such signals was given by McSharry et al. (2003) McSharry PE, Clifford GD, Tarassenko L, Smith LA. A dynamical model for generating synthetic electrocardiogram signals. IEEE Trans Biomed Eng. 2003; 50(3):28994. http://dx.doi.org/10.1109/TBME.2003.808805. PMid:12669985.
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. They proposed a dynamical model that generates a trajectory in the threedimensional statespace given by three coupled ordinary differential equations (ODE). The displacement around the “attracting limit cycle of unit radius” describes the ECG signal for each RRinterval ( McSharry et al., 2003 McSharry PE, Clifford GD, Tarassenko L, Smith LA. A dynamical model for generating synthetic electrocardiogram signals. IEEE Trans Biomed Eng. 2003; 50(3):28994. http://dx.doi.org/10.1109/TBME.2003.808805. PMid:12669985.
http://dx.doi.org/10.1109/TBME.2003.808...
). ECG characteristic waves are events with fixed angles in relation to the unit circle, given by
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) is given by
This dynamical model yields realistic signals when compared to real ECG signals ( McSharry et al., 2003 McSharry PE, Clifford GD, Tarassenko L, Smith LA. A dynamical model for generating synthetic electrocardiogram signals. IEEE Trans Biomed Eng. 2003; 50(3):28994. http://dx.doi.org/10.1109/TBME.2003.808805. PMid:12669985.
http://dx.doi.org/10.1109/TBME.2003.808...
). By setting parameters
Some specific features of the heart rate can also be set, such as mean and standard deviation, besides spectral properties. Generated waveforms are similar to the 12lead ECG lead I. Although it is possible to produce multilead signals ( McSharry et al., 2003 McSharry PE, Clifford GD, Tarassenko L, Smith LA. A dynamical model for generating synthetic electrocardiogram signals. IEEE Trans Biomed Eng. 2003; 50(3):28994. http://dx.doi.org/10.1109/TBME.2003.808805. PMid:12669985.
http://dx.doi.org/10.1109/TBME.2003.808...
), in this work they were not considered.
In order to set parameters of the proposed method and perform experiments for validation, twenty synthetic signals were generated using the described model. Model parameters and features of the generated ECG signals are summarized in Table 1 and Table 2 . All signals were sampled at
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), unlike the most stateoftheart methods which focus on pure sinusoidal noise. So, in addition to the fundamental frequency, harmonics interferences were also considered ( Costa and Tavares, 2009 Costa MH, Tavares MC. Removing harmonic power line interference from biopotential signals in low cost acquisition systems. Comput Biol Med. 2009; 39(6):51926. http://dx.doi.org/10.1016/j.compbiomed.2009.03.004. PMid:19376509.
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).
ECG synthetic signals configuration using the model described in this section. Parameters:
ECG synthetic signals configuration using the model described in this section. Parameters:
Real ECG signals
In order to validate the proposed method using real ECG signals that have been originally corrupted by PLI, the Challenge 2011 (Training Set A) database from Physionet was chosen ( Goldberger et al., 2000 Goldberger AL, Amaral LAN, Glass L, Hausdorff JM, Ivanov PC, Mark RG, Mietus JE, Moody GB, Peng CK, Stanley HE. PhysioBank, PhysioToolkit, and PhysioNet: components of a new research resource for complex physiologic signals. Circulation. 2000; 101(23):E21520. https://doi.org/10.1161/01.CIR.101.23.e215. PMid:10851218.
https://doi.org/10.1161/01.CIR.101.23.e...
). Their records were sampled at 500 Hz with
Discrete wavelet transform
The wavelet analysis has been applied to various problems in biomedical engineering including noise removal in ECG signals ( Agante and Sa, 1999 Agante PM, Sa JPM. ECG noise filtering using wavelets with softthresholding methods. Comput Cardiol. 1999; 26:5358. ; AlMahamdy and Riley, 2014 AlMahamdy M, Riley HB. Performance study of different denoising methods for ECG signals. Procedia Comput Sci. 2014; 37:32532. http://dx.doi.org/10.1016/j.procs.2014.08.048.
http://dx.doi.org/10.1016/j.procs.2014....
; Awal et al., 2014 Awal MA, Mostafa SS, Ahmad M, Rashid MA. An adaptive level dependent wavelet thresholding for ECG denoising. Biocybern Biol Eng. 2014; 34(4):23849. ; Bahoura and Ezzaidi, 2010 Bahoura M, Ezzaidi H. FPGAimplementation of waveletbased denoising technique to remove powerline interference from ECG signal. Inf Technol Appl Biomed (ITAB). In: Proceedings of the 10th IEEE International Conference; 2010 Nov 35; Corfu, Greece. New Jersey: IEEE; 2010. p. 14. ; Chouakri et al., 2006 Chouakri SAS, BereksiReguig AF, Fokapu O. ECG signal smoothing based on combining wavelet denoising levels. Asian J Inf Technol. 2006; 5(6):66677. ; Garg et al., 2011 Garg G, Gupta S, Singh V, Gupta JRP, Mittal AP. Identification of optimal waveletbased algorithm for removal of power line interferences in ECG signals. In: Proceedings of the India International Conference on Power Electronics; 2011 Jan 2830; New Delhi, India. New Jersey: IEEE; 2011. p. 15. http://dx.doi.org/10.1109/IICPE.2011.5728090.
http://dx.doi.org/10.1109/IICPE.2011.57...
; GermánSalló, 2010 GermánSalló Z. Nonlinear filtering in ECG signal denoising. Acta Univ Sapientiae Elec Mech Eng. 2010; 2:13645. ; Karthikeyan et al., 2012 Karthikeyan P, Murugappan M, Yaacob S. ECG signal denoising using wavelet thresholding techniques in human stress assessment. Int J Elec Eng Inf. 2012; 4(2):306. ; Li et al., 2009 Li S, Liu G, Lin Z. Comparisons of wavelet packet, lifting wavelet and stationary wavelet transform for denoising ECG. In: Proceedings of the 2nd IEEE International Conference on Computer Science and Information Technology (ICCSIT 2009); 2009 Aug 811; Beijing, China; New Jersey: IEEE; 2009. p. 4914. ; Patil and Chavan, 2012 Patil PB, Chavan MS. A wavelet based method for denoising of biomedical signal. In: Proceedings of International Conference on Pattern Recognition, Informatics and Medical Engineering (PRIME); 2012 Mar 2123; Salem, Tamilnadu, India. New Jersey: IEEE; 2012. p. 27883. http://dx.doi.org/10.1109/ICPRIME.2012.6208358.
http://dx.doi.org/10.1109/ICPRIME.2012....
; Poornachandra and Kumaravel, 2008 Poornachandra S, Kumaravel N. A novel method for the elimination of power line frequency in ECG signal using hyper shrinkage function. Digit Signal Process. 2008; 18(2):11626. http://dx.doi.org/10.1016/j.dsp.2007.03.011.
http://dx.doi.org/10.1016/j.dsp.2007.03...
; Üstündağ et al., 2012 Üstündağ M, Gökbulut M, Sengür A, Ata F. Denoising of weak ECG signals by using wavelet analysis and fuzzy thresholding. Netw Model Anal Health Inform Bioinform. 2012; 1(4):13540. http://dx.doi.org/10.1007/s1372101200155.
http://dx.doi.org/10.1007/s1372101200...
). Due to its better timefrequency resolution, it overcomes other classical methods, such as short time Fourier Transform, for instance ( Üstündağ et al., 2012 Üstündağ M, Gökbulut M, Sengür A, Ata F. Denoising of weak ECG signals by using wavelet analysis and fuzzy thresholding. Netw Model Anal Health Inform Bioinform. 2012; 1(4):13540. http://dx.doi.org/10.1007/s1372101200155.
http://dx.doi.org/10.1007/s1372101200...
). One of the advantages when using wavelets is the computational efficiency of Mallat’s pyramidal algorithm ( Mallat, 1989 Mallat SG. A theory for multiresolution signal decomposition: the wavelet representation. IEEE Trans Pattern Anal Mach Intell. 1989; 11(7):67493. http://dx.doi.org/10.1109/34.192463.
http://dx.doi.org/10.1109/34.192463 ...
). This algorithm is indeed a twochannel filter bank that splits the input signal in low and high frequencies by using quadrature mirror filters. The filters can be described through the wavelet
http://dx.doi.org/10.1109/34.192463 ...
):
where
and
where
Therefore, the wavelet decomposition output is a smooth signal representing the original one in a coarse way. In addition, the details are obtained when moving from a lower to a higher scale. Note that the smooth signal and details represent the similarity between the scaling and wavelet functions, according to Equations (7) and (6) , respectively. For an ECG signal, the approximation coefficients represent its smoothed version. On the other hand, detail coefficients capture abrupt changes, such as highfrequency noises. In order to reconstruct the signal
In the analysis step, the output wavelet filter bank frequency spectrum is divided into two octave bands. In each new decomposition level, the lowfrequency spectrum is again divided into two new octave bands, at the ideal cutoff frequencies, and so on, resulting in a logarithmical set of bandwidth ( GermánSalló, 2010 GermánSalló Z. Nonlinear filtering in ECG signal denoising. Acta Univ Sapientiae Elec Mech Eng. 2010; 2:13645. ). Therefore, if
http://dx.doi.org/10.1016/j.ymssp.2008....
). Therefore, the intervals are not exactly those mentioned before. Abrupt changes in the frequency intervals do not occur, but the filters frequency responses magnitude decreases gradually, tending to a constant value. Thus, leakage energy affects the frequency content for each DWT decomposition subband. Approximation coefficients are scattered higher than
Frequency response for the quadrature mirror analysis filters in Equations (2) (black line) and (3) (red line) for Symlet 8tap wavelet in three decomposition levels and 500 Hz sampling rate. (a) Level one. (b) Level two. (c) Level three.
Thresholding techniques
Classical methods for ECG denoising based on thresholding techniques present good performances ( AlMahamdy and Riley, 2014 AlMahamdy M, Riley HB. Performance study of different denoising methods for ECG signals. Procedia Comput Sci. 2014; 37:32532. http://dx.doi.org/10.1016/j.procs.2014.08.048.
http://dx.doi.org/10.1016/j.procs.2014....
; Garg et al., 2011 Garg G, Gupta S, Singh V, Gupta JRP, Mittal AP. Identification of optimal waveletbased algorithm for removal of power line interferences in ECG signals. In: Proceedings of the India International Conference on Power Electronics; 2011 Jan 2830; New Delhi, India. New Jersey: IEEE; 2011. p. 15. http://dx.doi.org/10.1109/IICPE.2011.5728090.
http://dx.doi.org/10.1109/IICPE.2011.57...
; Patil and Chavan, 2012 Patil PB, Chavan MS. A wavelet based method for denoising of biomedical signal. In: Proceedings of International Conference on Pattern Recognition, Informatics and Medical Engineering (PRIME); 2012 Mar 2123; Salem, Tamilnadu, India. New Jersey: IEEE; 2012. p. 27883. http://dx.doi.org/10.1109/ICPRIME.2012.6208358.
http://dx.doi.org/10.1109/ICPRIME.2012....
; Poornachandra and Kumaravel, 2008 Poornachandra S, Kumaravel N. A novel method for the elimination of power line frequency in ECG signal using hyper shrinkage function. Digit Signal Process. 2008; 18(2):11626. http://dx.doi.org/10.1016/j.dsp.2007.03.011.
http://dx.doi.org/10.1016/j.dsp.2007.03...
). Basically, in such methods, the goal is to estimate the signal
http://dx.doi.org/10.1093/biomet/81.3.4...
). For this purpose, the DWT is applied to
In order to implement the wavelet shrinkage method, it has considered the Symlet 8 wavelet with three DWT decomposition levels and universal threshold (given by
http://dx.doi.org/10.1109/IICPE.2011.57...
; Patil and Chavan, 2012 Patil PB, Chavan MS. A wavelet based method for denoising of biomedical signal. In: Proceedings of International Conference on Pattern Recognition, Informatics and Medical Engineering (PRIME); 2012 Mar 2123; Salem, Tamilnadu, India. New Jersey: IEEE; 2012. p. 27883. http://dx.doi.org/10.1109/ICPRIME.2012.6208358.
http://dx.doi.org/10.1109/ICPRIME.2012....
). The choice of the wavelet function order and the number of decomposition levels are justified since they are the same used by the proposed method.
Notch filter
McManus et al. (1993) McManus CD, Neubert K, Cramer E. Characterization and Elimination of AC Noise in Electrocardiograms: A Comparison of Digital Filtering Methods. Comput Biomed Res. 1993; 26(1):4867. http://dx.doi.org/10.1006/cbmr.1993.1003. PMid:8444027.
http://dx.doi.org/10.1006/cbmr.1993.100...
present four categories of digital filters for PLI removal: lowpass, notchrejection, adaptive and global. For the implementation of the narrowbandrejection filter (notch) it is considered a recursive filtering that includes a twopole and twozero filter. The filter output is given by
http://dx.doi.org/10.1006/cbmr.1993.100...
, apud Lynn, 1971 Lynn PA. Recursive digital filters for biological signals. Med Biol Eng. 1971; 9(1):3743. http://dx.doi.org/10.1007/BF02474403. PMid:5580486.
http://dx.doi.org/10.1007/BF02474403 ...
).
In order to compare the proposed method with a classical approach, the recursive notch filter was selected. Lynn (1971) Lynn PA. Recursive digital filters for biological signals. Med Biol Eng. 1971; 9(1):3743. http://dx.doi.org/10.1007/BF02474403. PMid:5580486.
http://dx.doi.org/10.1007/BF02474403 ...
apud McManus et al., (1993) McManus CD, Neubert K, Cramer E. Characterization and Elimination of AC Noise in Electrocardiograms: A Comparison of Digital Filtering Methods. Comput Biomed Res. 1993; 26(1):4867. http://dx.doi.org/10.1006/cbmr.1993.1003. PMid:8444027.
http://dx.doi.org/10.1006/cbmr.1993.100...
, set
Considering that the objective of this work is to introduce a new method that overcomes the thresholding techniques, the results were compared to the ones obtained by a classical approach.
Evaluation metrics
In the literature, many objective measures are proposed to assess denoising techniques. One of them is the SNR, given by
http://dx.doi.org/10.1007/s1372101200...
):
The measures presented before are appropriate for synthetic ECG signals, but not for real signals, since, in that case, there is no prior access to noiseless ECG signals samples. In this way, two metrics, proposed by Li et al. (2014) Li Q, Rajagopalan C, Clifford GD. A machine learning approach to multilevel ECG signal quality classification. Comput Methods Programs Biomed. 2014; 117(3):43547. http://dx.doi.org/10.1016/j.cmpb.2014.09.002. PMid:25306242.
http://dx.doi.org/10.1016/j.cmpb.2014.0...
, are used: the relative QRS complexes energy, given by
Statistical analysis
In order to evaluate whether the differences among the means in the experimental results are merely due to some random samples in the population, it is used the KruskalWallis test. In this statistical test, ranks are used instead of the original observations. Firstly, all observations are ranked together and then the sum of the ranks is computed for each sample by means of the equation:
http://dx.doi.org/10.1080/01621459.1952...
).
http://dx.doi.org/10.1080/01621459.1952...
). In our case, the null hypothesis is that there is no significant difference among the tested methods. In this work
Proposed method
According to equation (1) , the ECG signal represented by
In the wavelet domain, the signal
http://dx.doi.org/10.1016/j.ymssp.2008....
). It results in a band overlap with frequency content close to
http://dx.doi.org/10.1016/j.ymssp.2008....
), i.e., besides the expected frequency components, other frequencies also appear in the decomposed signal. Peng et al. (2009) Peng Z, Jackson M, Rongong J, Chu F, Parkin R. On the energy leakage of discrete wavelet transform. Mech Syst Signal Process. 2009; 23(2):33043. http://dx.doi.org/10.1016/j.ymssp.2008.05.014.
http://dx.doi.org/10.1016/j.ymssp.2008....
solved this problem by resampling the signal when the frequency content of interest is in the neighborhood of
Choosing
As suggested by Peng et al. (2009) Peng Z, Jackson M, Rongong J, Chu F, Parkin R. On the energy leakage of discrete wavelet transform. Mech Syst Signal Process. 2009; 23(2):33043. http://dx.doi.org/10.1016/j.ymssp.2008.05.014.
http://dx.doi.org/10.1016/j.ymssp.2008....
, the upper limit for the approximation coefficients is higher than 25 Hz, which is the frequency of interest. Therefore, setting the sampling rate at 125 Hz is suitable. Obviously, for other sampling rates that are integer multiple of 125 Hz, the ECG signal and PLI noise can also be separated, but for higher decomposition levels. Nevertheless, for the experiments performed in this work the best results were obtained at a sampling frequency of 500 Hz. In Table 4 it is shown the frequency distribution in each decomposition level for such sampling rate. Columns two and three show the frequency range for ideal cutoff frequencies according to the range shown in the Figure 1 . Columns four and five show the real ranges, which are approximated values, obtained by analyzing the frequency response with the Symlet 8tap. In the column six are presented the approximate band overlap ranges, considering the quadrature mirror analysis filters from Equations (4) and (5) .
Frequency distribution for the wavelet decomposition of a signal sampled at 500 Hz considering a 3 dB cutoff frequency, according to Figure 1 .
In a noisefree ECG signal reconstruction, detail coefficients are not so important, since they do not have relevant information about the ECG signal waveform, as shown in Table 4 . Therefore, in order to obtain the signal
The proposed method can be summarized in four steps: 1) The ECG signal is sampled at
The choice of the parameter
Results
The wavelet function choice
When applying the wavelet transform, besides the decomposition level choice discussed in the last section, it is also important to choose the wavelet function that best fits the signal. When ECG is the subject and threshold based methods are used, some researchers prefer Symlet wavelets because their scaling function resembles more its waveform ( Awal et al., 2014 Awal MA, Mostafa SS, Ahmad M, Rashid MA. An adaptive level dependent wavelet thresholding for ECG denoising. Biocybern Biol Eng. 2014; 34(4):23849. ; Chouakri et al., 2006 Chouakri SAS, BereksiReguig AF, Fokapu O. ECG signal smoothing based on combining wavelet denoising levels. Asian J Inf Technol. 2006; 5(6):66677. ; Karthikeyan et al., 2012 Karthikeyan P, Murugappan M, Yaacob S. ECG signal denoising using wavelet thresholding techniques in human stress assessment. Int J Elec Eng Inf. 2012; 4(2):306. ; Li et al., 2009 Li S, Liu G, Lin Z. Comparisons of wavelet packet, lifting wavelet and stationary wavelet transform for denoising ECG. In: Proceedings of the 2nd IEEE International Conference on Computer Science and Information Technology (ICCSIT 2009); 2009 Aug 811; Beijing, China; New Jersey: IEEE; 2009. p. 4914. ). Good results are also found using Daubechies wavelets ( Karthikeyan et al., 2012 Karthikeyan P, Murugappan M, Yaacob S. ECG signal denoising using wavelet thresholding techniques in human stress assessment. Int J Elec Eng Inf. 2012; 4(2):306. ; Patil and Chavan, 2012 Patil PB, Chavan MS. A wavelet based method for denoising of biomedical signal. In: Proceedings of International Conference on Pattern Recognition, Informatics and Medical Engineering (PRIME); 2012 Mar 2123; Salem, Tamilnadu, India. New Jersey: IEEE; 2012. p. 27883. http://dx.doi.org/10.1109/ICPRIME.2012.6208358.
http://dx.doi.org/10.1109/ICPRIME.2012....
; Üstündağ et al., 2012 Üstündağ M, Gökbulut M, Sengür A, Ata F. Denoising of weak ECG signals by using wavelet analysis and fuzzy thresholding. Netw Model Anal Health Inform Bioinform. 2012; 1(4):13540. http://dx.doi.org/10.1007/s1372101200155.
http://dx.doi.org/10.1007/s1372101200...
) and Coiflet ( Agante and Sa, 1999 Agante PM, Sa JPM. ECG noise filtering using wavelets with softthresholding methods. Comput Cardiol. 1999; 26:5358. ; Karthikeyan et al., 2012 Karthikeyan P, Murugappan M, Yaacob S. ECG signal denoising using wavelet thresholding techniques in human stress assessment. Int J Elec Eng Inf. 2012; 4(2):306. ). On the other hand, Poornachandra and Kumaravel (2008) Poornachandra S, Kumaravel N. A novel method for the elimination of power line frequency in ECG signal using hyper shrinkage function. Digit Signal Process. 2008; 18(2):11626. http://dx.doi.org/10.1016/j.dsp.2007.03.011.
http://dx.doi.org/10.1016/j.dsp.2007.03...
compared some wavelet families with Mayer’s wavelet and conclude that the last one is better. Commonly, each method uses different thresholding techniques and they have influence on the wavelet function choice. However, there is some agreement about the use of Daubechies and Symlet wavelets. As the proposed method does not use thresholding techniques, the choice of wavelet function can be made by analyzing the results of experiments using the synthetic signals from Table 1 and Table 2 . Preliminary experiments with the proposed method showed that the relative error obtained when using Symlets is smaller than the one using Daubechies wavelet functions. Furthermore, it was noted that higher wavelet order leads to better result. However, runtime increases substantially.
For instance, the difference between the relative errors metrics, for the synthetic signal
Figure 2 shows the boxplots of the experiments for denoising synthetic signals with worse SNR:
Boxplot for several Symlet wavelet orders: (a) relative error metrics boxplot, (b) runtime.
Experiments
In order to validate the proposed method, evaluation measures were computed for each synthetic signal. According to the analysis in last section, Symlet 8 was used for simulations. Superscripts PM, TT and NF refer to proposed method, thresholding technique and notch filter, respectively.
Analyzing column eight in Table 5 , it can be seen a significant
Results for the proposed method (PM), thresholding technique (TT) and notch filter (NF) applied to synthetic ECG signal.
In Figure 3 , one can see the results in time and frequency domain, when applying the denoising methods for signal
Analysis display for signal
Table 6 shows results obtained by the proposed method, thresholding technique and notch filter for real signals. Comparing the original values in fourth column of Table 3 with the ones from the eighth to the tenth columns of Table 6 , it is noted that the frequencies over 25 Hz are less relevant for the denoised ECG signal than in the noisy ECG for all analyzed signals.
Results for the proposed method, thresholding technique and notch filter applied to real ECG signals. PSD column is the sum of the power spectrum density for frequencies over 25 Hz.
Discussion
Comparing the proposed method results to the ones obtained with hard thresholding method, it can be seen that the proposed method was worse than hard thresholding only for
By means of the KruskalWallis test, we conclude that there exists significantly statistical difference for at least two methods. In comparison to notch filter, the proposed method was better for all measures. However, the proposed method and the thresholding technique have a similar performance in statistical terms.
Note, from Figure 3 (f), that the energy of the QRS complexes remains practically unchanged when compared to the original. The original signal energy is close to
For real ECG signals, from Table 6 , it is notorious that the proposed method reached better results for all signals, except for record 1086219 with respect to
http://dx.doi.org/10.1109/97.475823 ...
). In comparison to notch filter, the proposed method obtained better results for all signals. It is noteworthy that notch filter performed the worst for all quality assessment tests.
From KruskalWallis test results, it is noted that only for the
From Figure 4 , one can observe that thresholding technique and notch filter removed the PLI only for some segments in the observed ECG signal, leaving the others attenuated. Hereby, the result for record 1105115 obtained by the proposed method is much better ( Table 6 , fifth row) than the other methods, since the high frequency noise (180 Hz, see spectrogram in Figure 4 ) was not removed by the thresholding technique and notch filter. Note that 180 Hz is 2nd harmonic frequency of 60 Hz.
(a) Raw ECG record 1105115 and (b) its spectrogram. Denoised ECG signal obtained by (c) proposed method, (e) thresholding technique and (g) notch filter and their spectrograms (d), (f) and (h), respectively.
Although the proposed method have obtained better results for the most of the analyzed signals, it is important to note that it depends on ECG signals sampling rate. So, one must be careful on the sampling rate and DWT decomposition level choices, since these parameters have great influence in the estimated signals quality, according to steps 1 and 4.2 of the proposed method. When, by technical reasons, the sampling rate cannot be changed, decomposition level must be chosen in such a way that a minimum amount of noise crosses into the signal subband.
Other limitation of the proposed method refers to the frequency content removed. In a scenario where frequencies over 34.60 Hz (see Table 4 ) are relevant, detail coefficients in the first level can be retained (frequencies in the range 111.40 to 250 Hz). Even so, PLI noise is removed. Though, in any case, the frequency content around 50/60 Hz is lost. In this way, the cardiac disorders that generate frequencies into the interval from 34.60 to 111.40 Hz are despised. It is essential to note that bandwidth mentioned in Table 4 can be distinct, provided that other cutoff frequency is considered. Therefore, the frequencies higher than 34.60 Hz are preserved in the reconstructed ECG signal.
In overview, in this paper it was proposed a new method for PLI noise removal based on the wavelet transform without the use of thresholding techniques. For such purpose, it was used a filter bank architecture implemented by the multiresolution analysis that allows splitting a signal in frequency subbands. By setting the sampling rate in 500 Hz, it is possible to separate PLI noise from ECG signal in distinct frequency subbands by using the wavelet representation. In order to choose this sampling rate, the energy leakage was considered, such that, for a DWT decomposition level, the frequency content of interest was close to half of the maximum signal frequency. Therefore, by zeroing detail coefficients, the ECG signal is reconstructed using only the approximation coefficients, obtaining a denoised ECG.
Energy conservation analysis for each cardiac cycle showed that the proposed method does not insert distortion in the estimated ECG signals. For real ECG signals, it was noted that the estimated QRS complexes waveforms are smooth and keep the expected morphology. On the other side, the thresholding technique added abrupt changes in some QRS complexes for records 1086219 and 2209843. Besides, other advantage of the proposed method is that there is no computational requirement for a threshold computation.
Although the proposed method depends on the sampling rate, it can be applied to other databases, with sampling rates different from a multiple of 125 Hz, since the signals resampling are considered. Finally, the proposed method can be applied for denoising other signals, with frequency content known in a specific range. In future works such applications will be considered.

How to cite this article: Oliveira BR, Duarte MAQ, Abreu CCE, Vieira Filho J. A waveletbased method for powerline interference removal in ECG signals. Res Biomed Eng. 2018; 34(1):. DOI: 10.1590/24464740.01817.
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Publication Dates

Publication in this collection
Jan 2018
History

Received
20 Apr 2017 
Accepted
18 Mar 2018