ElectroCardioGram (ECG) signals are widely used for diagnostic purposes. However, it is well known that these recordings are usually corrupted with different type of noise/artifacts which might lead to misdiagnosis of the patient. This paper presents the design and novel use of Infinite Impulse Response (IIR) filter based Discrete Wavelet Transform (DWT) for ECG denoising that can be employed in ambulatory health monitoring applications. The proposed system is evaluated and compared in terms of denoising performance as well as the computational complexity with the conventional Finite Impulse Response (FIR) based DWT systems. For this purpose, raw ECG data from MIT-BIH arrhythmia database are contaminated with synthetic noise and denoised with the aforementioned filter banks. The results from 100 Monte Carlo simulations demonstrated that the proposed filter banks provide better denoising performance with fewer arithmetic operations than those reported in the open literature

Coskun, A.

Eminaga, Y.

Kale, I.

ElectroCardioGram (ECG) signals are usually corrupted with various types of artifacts which degrade the signal quality and might lead to misdiagnosis. The wavelet denoising technique is widely studied in the artifact removal literature which employs conventional Finite Impulse Response (FIR) wavelet filter banks for decomposing, thresholding and reconstructing the noisy signal to obtain high fidelity and clean ECG signal. However, the use of high order FIR wavelet filters increases the hardware complexity and cost of the system. This paper presents novel hybrid Infinite Impulse Response (IIR)/FIR Discrete Wavelet Transform (DWT) filter banks that can be employed in ambulatory health monitoring applications for denoising purposes. The proposed systems are evaluated and compared to the conventional FIR based DWT systems in terms of the computational complexity as well as the denoising performance. The results from 100 Monte Carlo simulations demonstrated that the proposed filter banks provide better denoising performance with fewer arithmetic operations than those reported in the open literature

WestminsterResearch

Hybrid IIR/FIR Wavelet Filter Banks for ECG Signal Denoising

WestminsterResearchhttp://www.westminster.ac.uk/westminsterresearch IIR Wavelet Filter Banks for ECG Signal DenoisingEminaga, Y., Coskun, A. and Kale, I. This is a copy of the author’s accepted version of a paper subsequently to be published in the proceedings of the 22nd IEEE International Conference on Signal Processing: Algorithms, Architectures, Arrangements, and Applications (SPA). Poznan, Poland, 19 - 21 Sep 2018.The final published version will be available online at:https://doi.org/10.23919/SPA.2018.8563418© 2018 IEEE . Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.The WestminsterResearch online digital archive at the University of Westminster aims to make the research output of the University available to a wider audience. Copyright and Moral Rights remain with the authors and/or copyright owners.Whilst further distribution of specific materials from within this archive is forbidden, you may freely distribute the URL of WestminsterResearch: ((http://westminsterresearch.wmin.ac.uk/).In case of abuse or copyright appearing without permission e-mail repository@westminster.ac.ukIIR Wavelet Filter Banks for ECG Signal DenoisingYaprak Eminaga, Adem Coskun, and Izzet KaleApplied DSP and VLSI Research GroupUniversity of Westminster, London, W1W 6UW, United KingdomEmail: y.eminaga@my.westminster.ac.uk, a.coskun@westminster.ac.uk, kalei@westminster.ac.ukAbstract—ElectroCardioGram (ECG) signals are widely usedfor diagnostic purposes. However, it is well known thatthese recordings are usually corrupted with different type ofnoise/artifacts which might lead to misdiagnosis of the patient.This paper presents the design and novel use of Infinite ImpulseResponse (IIR) filter based Discrete Wavelet Transform (DWT)for ECG denoising that can be employed in ambulatory healthmonitoring applications. The proposed system is evaluated andcompared in terms of denoising performance as well as thecomputational complexity with the conventional Finite ImpulseResponse (FIR) based DWT systems. For this purpose, raw ECGdata from MIT-BIH arrhythmia database are contaminated withsynthetic noise and denoised with the aforementioned filter banks.The results from 100 Monte Carlo simulations demonstrated thatthe proposed filter banks provide better denoising performancewith fewer arithmetic operations than those reported in the openliterature.Keywords—ECG denoising, Discrete Wavelet Transform, FIRwavelets, IIR wavelets.I. INTRODUCTIONThe ECG signals are usually contaminated with variousnoise where the noise and signal spectra overlap and theconventional filtering techniques are insufficient to removethis noise. DWT is a popular tool in the field of non-stationary signal processing that provides simultaneous timeand frequency information, and has been used to detect suchoverlapping noise. In ECG denoising literature a vast amountof research employed FIR filter banks with various waveletfamilies, most popular ones being the Daubechies such asHaar, db2, and db4, Symmlets and Coiflets [1]–[3]. On theother hand, IIR wavelet filter bank studies are less extensiveand limited to image processing and compressing applications[4], [5]. This paper presents the design of IIR DWT filterbanks and their novel application in ECG signal denoising.To the best knowledge of the authors’, this is a first in theopen literature and the results showed that the proposed IIRDWT filter banks achieve higher output Signal-to-Noise Ratio(SNR) and lower Mean Square Error (MSE) with reducedarithmetic operation complexity compared to the conventionalFIR wavelets.Section II provides brief information regarding the theoryof IIR wavelet design followed by the details of the designedIIR wavelets. Section IV introduces the wavelet thresholdingtechnique employed and the noisy test data generated. Com-parative analysis on the noise suppression performance of theproposed IIR and FIR wavelets for different noise scenariosare presented in Section V. Finally, Section VI presents theconclusions.II. IIR WAVELET ANALYSIS FILTER BANK PROPERTIESThe analysis part of a two channel Perfect Reconstruction(PR) IIR filter bank can be realized with a halfband lowpassand a halfband highpass filter denoted by H0(z) and H1(z),respectively. These filters are based on the parallel connectionof two real all-pass filters [6], [7] and 1-level transform matrixfor the analysis filter bank is given in (1).H (z) =[H0 (z)H1 (z)]=1√2[A0(z2)+ z−1A1(z2)A0(z2)− z−1A1 (z2)], (1)where A0(z) and A1(z) are M th order allpass filters with ageneral transfer function,A (z) = z−MM∑m=0αmzmM∑m=0αmz−m(2)As it can be observed from (1), H0(z) and H1(z) are powercomplementary filters, since they satisfy the following prop-erty.|H0 (z)|2 + |H1 (z)|2 = 1 (3)The scaling and wavelet functions associated with the afore-mentioned filters, can be achieved by iterating the filter bank Jtimes on its lowpass branch as shown in (4). This will result intransfer functions Φ (z) and Ψ (z) with lowpass and bandpassspectrum where their impulse responses are the scaling (φ (n))and wavelet (ψ (n)) functions, respectively.Φ (z) =J−1∏j=0H0(z2j)Ψ (z) = H1(z2j−1) J−2∏j=0H0(z2j) (4)It is well known that, the regularity of wavelets defines thesmoothness of the wavelet function and has a crucial effectfor noise reduction applications. It is directly related to thewavelet’s vanishing moments which is the number of timesthe wavelet spectrum vanishes (goes to zero) at ω = 0 i.e∣∣Ψ(ejω)∣∣ω=0= 0 where z = ejω. Thus, the aforementionedH0 (z) and H1 (z) needs to be designed with an additionalflatness condition as shown in (5) [8].∂k∣∣H1 (ejω)∣∣∂ωk∣∣∣∣∣ω=0=∂k∣∣H0 (ejω)∣∣∂ωk∣∣∣∣∣ω=pi= 0 (5)for k = 0, 1, ...K − 1, where K corresponds to the number ofzeros of H1 (z) at z = 0 and H0 (z) at z = −1 i.e. Nyquistfrequency. This design procedure can be reduced to the designof H0 (z) due to the power complementary properties givenin (3). For a given filter order, a trade of between frequencyresolution and wavelet regularity exists. Therefore, it is criticalto identify needs of the application and select the best possiblefrequency selectivity for a given flatness condition [6].III. IIR WAVELET ANALYSIS FILTER BANK DESIGNIn this study, IIR wavelet design methodology introducedby Zhang et. al [6] is adopted for implementing IIR waveletfilters with 3 and 5 vanishing moments and are referred toas ilet3 and ilet5, respectively in the rest of this document.Both wavelets filters are designed as maximally flat filters inorder to achieve the maximum number of zeros at the Nyquistleading to the maximum possible smoothness of the scalingand wavelet functions. The number of vanishing momentsare selected in order to closely match the most commonlyused wavelet basis functions in ECG denoising applicationsincluding, db2, and db4 with 2 and 4 vanishing moments,respectively. Recalling (1), H0 (z) can be re-written as,H0 (z) =12A0(z2) (1 + z−1U(z2))(6)where U(z) is an allpass filter with a general transfer functiongiven in (2). For ilet5 wavelets U(z) is chosen to be a secondorder filter with real coefficients a2, a1, and a0 = 1. Thus, forM = 2, its transfer function is expressed as,U(z2)=A1(z2)A0 (z2)= z−4a0 + a1z2 + a2z4a0 + a1z−2 + a2z−4(7)The frequency response of H0 (z) is calculated by evaluat-ing (6) on the unit circle and the magnitude response is givenby, ∣∣H0 (ejω)∣∣ = cos θ (ω)2(8)where θ(ω) is the phase response of z−1U(z2). Therefore,for ilet5, θ(ω) and∣∣H0 (ejω)∣∣ is respectively computed as,θ (ω) = −2 tan−1 sin(5ω2)+ a1 sin(ω2)− a2 sin ( 3ω2 )cos(5ω2)+ a1 cos(ω2)+ a2 cos(3ω2) (9)∣∣H0 (ejω)∣∣ = cos ( 5ω2 )+ a1 cos (ω2 )+ a2 cos ( 3ω2 )√3 + 2a1 (1 + a2) cos (2ω) + 2a2 cos (4ω)(10)As mentioned before, the smoothness of the wavelet func-tion is determined by the number of zeros at the Nyquist,which is computed by substituting the numerator of (10) into(5). Then, filter coefficients a1 = 10 and a2 = 5 are calculatedby solving the linear equations obtained. The same steps areapplied for ilet3 with M = 1 and K = 3. This results ina1 = 3. Following (7), the poles of U(z) that lies inside theunit circle corresponds to the poles of A1(z) and the polesoutside the unit circle corresponds to the zeros of A0(z).By assigning the poles correctly, two stable allpass filters areobtained. The magnitude responses and pole-zero locations of(a)3 3(b)(c)55(d)Fig. 1. ilet3; (a) Magnitude response and (b)Pole-Zero locations. ilet5; (c)Magnitude response and (d) Pole-Zero locations.(a) (b)Fig. 2. Scaling (φ (n)) and Wavelet (ψ (n)) functions of (a) ilet3 and (b)ilet5 after 8 iterations.H0(z) and H1(z) and corresponding impulse responses, φ(n)and ψ (n) for ilet3 and ilet5 are presented in Fig. 1 and Fig.2, respectively.IV. METHODThere is various types of noise such as powerline interfer-ence, baseline wander, and muscle contraction artifacts thatare assumed to be additive and independent from the the ECGsignal which is generally modelled as xn (n) = xc (n)+e (n),where xn (n), xc (n), and e (n) are the noisy ECG, cleanECG and composite noise, respectively. Although powerlineinterference can be eliminated by a digital notch filter, thespectrum of other noise sources overlap with the spectrum ofthe ECG signal. In such circumstances, wavelet thresholdingcan be employed where the noisy signal is decomposedinto several levels, denoised and reconstructed [9]. For thisstudy, the noisy ECG signal is decomposed into 7 levels andeach of the detail coefficients (i.e. outputs of H1(z) at eachlevel) are thresholded using the soft thresholding method, inwhich the threshold is computed using the Rigorous SURE(Stein’s Unbiased Risk Estimator) criterion [10]. The baselinewander is removed by nullifying the finest level approximationcoefficients (i.e. H0(z) output at level 7) and the denoisedsignal is reconstructed from the thresholded detail coefficients.The thresholding method and threshold criterion is empiricallydetermined where soft thresholding is well-known for deliv-ering smoother outputs and the Rigorous SURE threshold se-lection scheme is known for successfully identifying the smalldetails of signal overlapped with noise. A good comparison ofdifferent threshold selection and thresholding methods can befound in [11].A. Generated ECG data and Synthetic Noise SourcesFour raw ECG records (’103’, ’105’, ’109’, and ’118’) arerandomly taken from the MIT-BIH arrhythmia database whichare resampled to 256 Hz. In order to obtain clean controldata, preprocessing stages are applied, including notch andhighpass filtering (cut-off frequency (fc) = 0.5 Hz), to remove60 Hz powerline interference and baseline wander, respec-tively. Then, the ElectroMyogram (EMG) interference (xe (n))is modelled as white Gaussian noise, whereas the baselinewander is modelled as additive combination of deterministicand random data with frequency content below 1 Hz as shownin (11).xbw (n) =P∑i=1sin(2pinfifs)+W (n) (11)where 0 < fi ≤ 1 for i = 1, 2, . . . , P , fs is the samplingfrequency and W (n) is lowpass filtered (fc = 1 Hz) whiteGaussian noise. Thus, the composite noise is obtained bye (n) = A(xe (n)+xbw (n)) where A is the input noise scalingfactor that is determined by the desired input SNR and iscomputed via;A =√√√√∑Nn=1 |xc (n)|2∑Nn=1 |e (n)|210−SNR/10 (12)B. Quantitative EvaluationThe ECG signal denoising performance of ilet3 and ilet5as well as Haar, db2, db4, sym4, and coif2 wavelet filterbanks are evaluated and compared by computing the SNRimprovement and MSE which are obtained from;SNRimp =∑Nn=1 |xn (n)− xc (n)|2∑Nn=1 |xd (n)− xc (n)|2MSE =1NN∑n=1|xd (n)− xc (n)|2(13)where xd (n) is the denoised ECG signal.V. RESULTS AND DISCUSSIONSFour records (’103’, ’105’, ’109’, and ’118’) are con-taminated by adding the synthetically generated EMG andbaseline wander with SNR ranging from −12 to 20 dB. Fig. 3Fig. 3. Top to bottom;10 seconds of clean record ’103’,EMG noise, BaselineWander, Noisy ECG, and Denoised ECG.presents (top to bottom) the clean ECG record ’103’, generatedsynthetic EMG and baseline wander, noisy ECG contaminatedwith composite noise with SNR = 4 dB, and finally thedenoised ECG with ilet5 wavelet filter bank. For each datarecord and at each SNR, 100 Monte Carlo Simulations areperformed and the average SNR and MSE are computed.Results for the noisy record ’103’ are shown in Fig. 4. As it canbe observed, the ilet5 wavelet filter bank provides the highestSNR improvement and the lowest MSE when compared toothers, where ilet3 provides the second best results. In TableI, the average SNR improvement (in dB) figures obtained forilet3, ilet5, db4 and Haar wavelets are also presented forfour noisy ECG records. As expected, ilet5 provides the bestresults compared to the FIR wavelets, followed by ilet3 bothunder high and relatively low noise power. This is due tothe better frequency selectivity achieved with the IIR waveletsdespite having lower vanishing moments,i.e. in the ilet3 case.Although, Haar wavelet is the simplest FIR wavelet filterwhich makes it desirable for power limited applications, itachieves the lowest denoising performance. On the otherhand, ilet3 filter with one distinct coefficient provides betterdenoising performance making it a favourable choice amongstthe others. For applications where the denoising performanceis critical and the power consumption can be compromisedthen the ilet5 can be employed which uses only two distinctcoefficients. In addition, Table II presents the average MSEresults where the ilet5 and ilet3 wavelets provide the twominimum MSE results. This is an indication of a relativelysmaller signal distortion after denoising which is a significantfactor for diagnostic applications. In terms of computationalcomplexity except from the Haar filter, rest of the FIR filtersemploy 4, 8 and 12 rational coefficients. Thus, based on theselected filter structure, the arithmetic and storage complexity-10 -5 0 5 10 15 20Input SNR, dB-22610SNRImprovement,dBRecord 103 + Composite Noiseilet3ilet5db2db4sym4Haarcoif2(a)-10 -5 0 5 10 15 20Input SNR, dB0.020.040.060.080.10.120.140.16MSEafterDenoisingRecord 103 + Composite Noise12 14 16 18 20024×10−3(b)Fig. 4. Average (a) SNR Improvement (dB), and (b) MSE, after wavelet denoising with ilet3, ilet5, db2, db4, sym4, Haar and coif2.TABLE ISNR IMPROVEMENT AFTER WAVELET DENOISING.Input SNR = -12 dB Input SNR = 4 dBilet3 ilet5 db4 Haar ilet3 ilet5 db4 Haar’103’ 13.07 13.92 12.18 9.49 9.13 9.4 8.72 5.55’105’ 13.71 14.58 12.72 9.67 9.21 9.90 8.72 5.32’109’ 13.92 14.92 12.98 9.68 10.18 11.38 9.20 5.27’118’ 13.68 14.42 12.56 9.61 8.24 9.34 6.93 4.72TABLE IIMSE AFTER WAVELET DENOISINGInput SNR = -12 dB Input SNR = 4 dBilet3 ilet5 db4 Haar ilet3 ilet5 db4 Haar’103’ 0.07 0.06 0.09 0.17 0.0046 0.0044 0.005 0.011’105’ 0.06 0.05 0.07 0.16 0.0045 0.0038 0.0049 0.011’109’ 0.12 0.098 0.15 0.17 0.0074 0.0056 0.0086 0.022’118’ 0.11 0.096 0.14 0.29 0.0101 0.0078 0.0129 0.022will always be higher for the FIR wavelets in comparison to theIIR wavelets. Also, it is a well known fact that for fixed-pointimplementations, FIR filters are more sensitive to coefficientquantization which require higher word-lengths compared toallpass based halfband polyphase IIR filters, further increasingthe system complexity.VI. CONCLUSIONSIn this paper, the novel use of IIR wavelet filter banksfor ECG signal denoising is presented. For this purpose, twomaximally flat and stable IIR wavelet filters, ilet3 and ilet5are designed. Both filters are computationally efficient whereilet3 and ilet5 employs one and two distinct coefficients,respectively that can be implemented with simple shift andadd operations without using costly multipliers. A comparativeanalysis of ECG signal denoising based on the aforementionedIIR wavelet filters and state-of-the-art FIR wavelet filters iscarried out. The denoising performance of all filter banks areevaluated through the generation of the synthetic noisy signalsand compared by means of the SNR improvement and theoutput MSE. The results obtained demonstrated that the IIRwavelets achieve the best ECG denoising performance with theleast signal distortion amongst the others with fewer arithmeticoperations. This study demonstrates that IIR wavelets canbe included in more sophisticated denoising applications inportable devices due to their better frequency selectivity withlesser arithmetic operations.ACKNOWLEDGMENTThe authors wish to thank the University of WestminsterFaculty of Science and Technology for the PhD Studentship.REFERENCES[1] Y. Eminaga, A. Coskun, and I. Kale, “Multiplier Free Implementationof 8-tap Daubechies Wavelet Filters for Biomedical Applications,” in2017 New Generation of CAS (NGCAS). IEEE, 2017, pp. 129–132.[2] S. Nagai, D. Anzai, and J. Wang, “Motion artefact removals for wearableECG using stationary wavelet transform,” Healthcare technology letters,vol. 4, no. 4, p. 138, 2017.[3] P. Shemi and E. Shareena, “Analysis of ECG signal denoising usingdiscrete wavelet transform,” in Engineering and Technology (ICETECH),2016 IEEE International Conference on. IEEE, 2016, pp. 713–718.[4] X. Zhang, W. Wang, T. Yoshikawa, and Y. Takei, “Design of IIRorthogonal wavelet filter banks using lifting scheme,” IEEE Transactionson Signal Processing, vol. 54, no. 7, pp. 2616–2624, 2006.[5] J. M. Abdul-Jabbar and R. W. Hmad, “Allpass-based design, multipli-erless realization and implementation of IIR wavelet filter banks withapproximate linear phase,” in Innovation in Information & Communi-cation Technology (ISIICT), 2011 Fourth International Symposium on.IEEE, 2011, pp. 118–123.[6] X. Zhang and T. Yoshikawa, “Design of orthonormal IIR wavelet filterbanks using allpass filters,” Signal Processing, vol. 78, no. 1, pp. 91–100, 1999.[7] S. Damjanovic and L. Milic, “Examples of orthonormal wavelet trans-form implementad with IIR filter pairs,” Proc. SMMSP 2005, Riga,Latvia, pp. 19–27, 2005.[8] C. Herley and M. Vetterli, “Wavelets and recursive filter banks,” IEEETransactions on Signal Processing, vol. 41, no. 8, pp. 2536–2556, 1993.[9] J. Gao, H. Sultan, J. Hu, and W.-W. Tung, “Denoising nonlinear timeseries by adaptive filtering and wavelet shrinkage: a comparison,” IEEESignal Processing Letters, vol. 17, no. 3, pp. 237–240, 2010.[10] D. L. Donoho and I. M. Johnstone, “Adapting to unknown smoothnessvia wavelet shrinkage,” Journal of the American Statistical Association,vol. 90, no. 432, pp. 1200–1224, 1995.[11] S. R. Messer, J. Agzarian, and D. Abbott, “Optimal wavelet denoisingfor phonocardiograms,” Microelectronics Journal, vol. 32, no. 12, pp.931–941, 2001.

IIR Wavelet Filter Banks for ECG Signal Denoising

https://westminsterresearch.westminster.ac.uk/download/015b2705673b1fbf54f1e2c76a1932977efac999bb19ecae7633f995cfd1696f/966047/iir_fir_wavelet.pdf

IIR Wavelet Filter Banks for ECG Signal Denoising

Abstract

Similar works

Full text

Available Versions

WestminsterResearch

WestminsterResearch