electrocardiogrambaselinewandersuppressionbasedonthe ...eprints.usq.edu.au/36130/1/wan...

Research ArticleElectrocardiogram Baseline Wander Suppression Based on theCombination of Morphological and Wavelet TransformationBased Filtering

Xiang-kui Wan123 Haibo Wu1 Fei Qiao1 Feng-cong Li 1 Yan Li4 Yue-wen Yan1

and Jia-xin Wei1

1Hubei Key Laboratory for High-efficiency Utilization of Solar Energy and Operation Control of Energy Storage SystemHubei University of Technology Wuhan 430068 China2Hubei Collaborative Innovation Center for High-efficiency Utilization of Solar Energy Hubei University of TechnologyWuhan 430068 China3Hubei Power Grid Intelligent Control and Equipment Engineering Technology Research Center Wuhan 430068 China4Faculty of Health Engineering and Sciences University of Southern Queensland Toowoomba QLD 4350 Australia

Correspondence should be addressed to Feng-cong Li 401103757qqcom

Received 13 August 2018 Revised 14 January 2019 Accepted 7 February 2019 Published 3 March 2019

Academic Editor Maria E Fantacci

Copyright copy 2019Xiang-kuiWan et alis is an open access article distributed under the Creative CommonsAttribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

One of the major noise components in electrocardiogram (ECG) is the baseline wander (BW) Effective methods for suppressingBW include the wavelet-based (WT) and the mathematical morphological filtering-based (MMF) algorithms However the Twaveform distortions introduced by the WTand the rectangulartrapezoidal distortions introduced by MMF degrade the qualityof the output signal Hence in this study we introduce a method by combining the MMF andWT to overcome the shortcomingsof both existingmethods To demonstrate the effectiveness of the proposedmethod artificial ECG signals containing a clinical BWare used for numerical simulation and we also create a realistic model of baseline wander to compare the proposed method withother state-of-the-art methods commonly used in the literature e results show that the BW suppression effect of the proposedmethod is better than that of the others Also the new method is capable of preserving the outline of the BW and avoidingwaveform distortions caused by the morphology filter thereby obtaining an enhanced quality of ECG

1 Introduction

Electrocardiogram (ECG) is an important clinical tool forheart disease diagnosis hence precision of ECG is a matterof life and death However the quality of the ECG signal isdegraded during acquisition due to the interferences in-cluding power line harmonics motion artifact and baselinewander (BW) which makes it difficult to identify the factorswhich reflect the characteristics of physiological activity Asa consequence interference suppression should be appliedbefore the analysis of ECG [1] Notably the most importantstep is BW suppression which produces a stable signal forsubsequent processing and for reliable visual interpretation

BW embedded in ECG is mainly caused by the move-ment and respiration of the patient consequently it appears

as low-frequency artifacts [2] Unfortunately although thehigh-pass filter is capable of suppressing BW the ECGwaveform distortion is inevitable because of the frequencyvariations of the ECG signal Hence a number of advancedBW suppression algorithms including linear low-pass filtersnonlinear filters polynomial interpolation wavelet filtersand mathematical morphological filters (MMF) are pro-posed [3ndash9]

Linear filters can effectively filter the high-frequencysignals but cannot remove the additive noise which has afrequency band similar to that of ECG signals Polynomialinterpolation depends on the accurate determination ofknots and may be unreliable during knot separation [10]As a nonlinear filtering technique MMF can obtain localshape features in signals by structuring the element

HindawiComputational and Mathematical Methods in MedicineVolume 2019 Article ID 7196156 7 pageshttpsdoiorg10115520197196156

sequences [11 12] However its applications may result inldquostep-likerdquo waveform distortions Wavelet transform(WT) has also been used in BW removal In [3] BW isestimated from the discrete WTcoefficients at level j and issubtracted from the original ECG signals WT methodexhibits relatively good effects for BW suppressionHowever this method causes T waveform distortions dueto the frequency overlaps between the high-scale ap-proximate coefficients and T wave e ECG signal isreconstructed by an inverse WT and the high-scale ap-proximate coefficients are set to zero thereby causing theT wave distortion [13]

is study introduces a combined algorithm (CA) ofMMF- and WT-based filtering for BW suppression e CAcan effectively preserve the outline of the BW and avoidwaveform distortions caused by morphology filters therebyobtaining an enhanced ECG quality

e study is organized as follows Section 2 describes thecombined filtering method while the simulation results areprovided and quantitatively analyzed in Section 3 Finallysummary and conclusions are drawn in Section 4

2 The Combined Method

Considering that the main focus of this study is BW sup-pression we model the contaminated ECG as the super-position of the real ECG and the BW and ignoring othertypes of interferences as follows

fCECG(n) fECG(n) + fBW(n) (1)

where fCECG fECG and fBW are the contaminated ECG-real ECG- and BW-function with respect to time index nrespectively All of the time functions in this study arediscrete because the implementation of filtering is focusedon digital processing e BW suppression is commonlyimplemented by cancellation ie

1113954fECG(n) fCECG(n)minus 1113954fBW(n) (2)

where the hat symbol 1113954 denotes the estimation of the un-derneath term e output error of this cancellation pro-cedure is given by

e(n) fECG(n)minus 1113954fECG(n) 1113954fBW(n)minusfBW(n) (3)

which indicates that the performance of BW suppression isdetermined by the estimator of fBW ie 1113954fBW To refine theestimator 1113954fBW we provide a staged framework whichcombines N different filtering technology e expression ofthis framework is shown as follows

1113954fBW(n) fF1 middot fF2 middot middot fFN( 1113857 fCECG(n)( 1113857 (4)

where fFn is the nth filter and operator middot denotes functioncomposition defined as follows

(f middot g)(x) f(g(x)) (5)

By choosing filters carefully the framework is capable ofcombining advantages of different filter implementationsand in this study we combine the MMF-based filter andWT-based filter

21 7e Morphological Filtering e shortcomings of thelinear BW suppression methods are caused by the nonlinearnature of the contaminated ECG Hence nonlinear pro-cessing methods are preferred and the MMF belongs to thiscategory which is capable of maintaining the shape of theinput signale objects of the morphological operations aresets and vectors for the clarity of descriptions hereaftervectors are denoted by lower case boldface letters and RN

denotes the real coordinate space of N dimensions ereflection of a set comprised of vectors is defined as

Ar

minusa ∣ a isin A (6)

while the translation is given by(A)z a + z ∣ a isin A (7)

and hence the dilation and erosion can be expressed asfollows

AoplusB z ∣ Br

( 1113857z capAneempty1113864 1113865

A⊖B z ∣(B)z subeA1113864 1113865(8)

e morphological filter is comprised of opening andclosing operators which can be expressed by dilation anderosion as follows

AB (A⊖B)oplusB (9)

A bullB (AoplusB)⊖B (10)

We can apply these morphological operators to a timefunction by treating the nminusf plane as a binary image andthe value of the pixels underneath the curve equals one egeometric interpretation of opening in equation (9) andclosing in equation (10) is sliding a given structuring elementalong with the signal from beneath and above respectivelySpecifically the result of opening comprises the highestpoints reached by any part of the structuring element whileclosing is comprised of the lowest ones Consequently thesemantic meaning of openingclosing is peak-suppressionpit-filling According to themodel shown in equation (1) thespiky fECG can be seen as the noise for fBW estimation andintuitively the combination of opening and closing is capableof smoothing the fluctuation introduced by the fECG eexpression of the estimator has the following form

fMMF fCECG( 1113857 12

fCECG S bull S( 1113857 + fCECG bull S S( 11138571113858 1113859

(11)

where S is the structuring element Let the output of the filterbe the estimation of fBW ie

1113954fBW fMMF fCECG( 1113857 (12)

the estimation of fECG can be obtained by cancellation1113954fECG fCECG minus 1113954fBW IminusfMMF( 1113857 fCECG( 1113857 (13)

where I denotes the identity operator ieI(f) f (14)

We test the estimator and the cancellation procedureusing Massachusetts Institute of Technology-Bostonrsquos Beth

2 Computational and Mathematical Methods in Medicine

Israel Hospital (MIT-BIH) arrhythmia database [14] (recordnumber 109) Shape and size of the chosen structuring el-ement are very important e shape of structuring elementshould be as similar as the filtered signal waveform needede ECG baseline wander is a low-frequency signal and itsshape is more approximate to the line segment So themorphological filters are with line segments as structuringelements And the height of linear structuring element haslittle effect on the results of mathematical morphologicalfiltering e size of structuring element directly determineswhether the noise can be better removed and whether therequired signal can be better retained e width of struc-tural element should be wider than the noise waveformremoved and narrower than the signal waveform needed tobe retained If the width of the structural element is toosmall the noise component cannot be eliminated well if thewidth of the structural element is too large some signals thatneed to be retained will be filtered e time duration ofcharacteristic waves of ECG is listed in Table 1

For ECG signals with BW the frequency range of BWnoise is slightly smaller than that of Twave that is the timewidth of baseline drift noise waveform is larger than that ofcharacteristic waveform of ECG signal As mentioned abovethe time width of T wave is 005ndash020 s when the samplingrate is 360Hz the sampling points are 360 times 02 72 So thewidth of structural elements selected by BW is 72 samplingpoints in this paper e result is shown in Figure 1

eoretically if morphological filtering with a largewidth of the structuring element is used to process the signaldirectly the BW is obtained Despite the high amplitude ofQRS wave the peaks and pits of its adjacent regions are alsoremoved during the simulation resulting in the distortion ofthe QRS waves and P-R segments

22 7e Combination of WT-Based Filter Although theMMF can track the slow drifting of the baseline wanderingstep-like shape shown in Figure 1(c) demonstrates that theestimated BW is still noisy Considering various degrees ofdistortions we adopt WT-based filtering to smooth theestimated BW

Smoothing BW signal can be regarded as the elimi-nation of high-frequency components and retention oflow-frequency ones and WT-based filtering is suitable forthis kind of task e estimated BW can be decomposedinto multiple scales in the context of WT considering theBW frequency ranges from 005Hz to 2Hz the compo-nents below 2Hz are preserved while the ones above 2Hzare replaced with zero Finally the smoothened BW signalcan be obtained by reconstruction using the inversewavelet transform

Here we choose coif3 as the wavelet function becauseits regularity and symmetry properties are better com-pared with other wavelets Also the coif3 is the mostwidely used wavelet function for ECG process For theECG signal of which the sampling frequency is 360Hz theBW signal is decomposed by the WT into seven scalesAfter decomposition the approximate frequency range foreach scale is shown in Table 2 where D represents the

detailed components (high-frequency components) of thesignal at the scale after wavelet decomposition and Arepresents the approximate components (low-frequencycomponents) at the scale e seventh approximatecomponent is reserved

We denote the WT-based filter as fWT and combine itwith fMMF according to the framework shown in equation(4) hence the expression of the combined filter (or BWestimator) can be written as follows

1113954fBW fWT middot fMMF( 1113857 fCECG( 1113857 (15)

and the estimated ECG is given by the followingcancellation

1113954fECG IminusfWT middot fMMF( 1113857 fCECG( 1113857 (16)

e entire block diagram of the combined algorithm ofthe MMF and WT is shown in Figure 2

3 Numerical Simulation

In real ECG recordings the exact ECG value and BW noiseare unknown which prevents one from analyzing algorithmperformance with precision Hence a simulated ECG signalplus BW noise is used to evaluate the effectiveness of the CAproposed in this study [15]

e generation of the simulated contaminated ECG isbased on equation (1) while fBW used here is collectedclinically and the simulated fECG is constructed by

fECG(n) 1113944m

fSHB(n + mT) (17)

where fSHB(n) is the waveform of a single heartbeat of whichthe duration is T and 1113936mfSHB(n + mT) is the periodicrepetition of the heartbeat waveform representing a simu-lated clean ECG signal where m isin Z+

e specific process of obtaining the artificial ECG(ie S) is described as follows

(1) One heartbeat of an ECG recording which is fromthe recording of number 119 in MIT-BIT ar-rhythmia database sampled at 360Hz in restingconditions is selected e clean ECG is formed byperiodic repetitions of a single beat at 1000 timese clean ECG segment used in the experiment issubsequently obtained An example is shown inFigure 3

(2) e second channel of the BW data from the MIT-BIH noise stress test database is selected as the BW[16] Figure 4 shows the chosen BW signal

e performance of the proposed method was evaluatedby themean square error (MSE) and the signal-to-noise ratio(SNR) which are defined as formulas (18) and (19)respectively

Table 1 Time duration of characteristic waves of ECG signal

Characteristic waves P wave QRS wave T waveTime duration (s) 008sim011 006sim010 005sim020

Computational and Mathematical Methods in Medicine 3

MSE 1N

sum

Nminus1

n0fECG(n)minus fECG(n)( )

2 (18)

SNR 10 times lgθ2

MSE( ) (19)

where θ2 is the variance of the ECG dened as

θ2 1N

sum

Nminus1

n0fECG(n)minusfECG( )

2 (20)

where fECG is the mean of the ECGe calculated values ofthe MSE and SNR for the articial contaminated ECG signalltered by the algorithms are listed in Table 3

e MSE value is small indicating a smaller error be-tween the ltered ECG and the clean ECG e distortionproduced by the lter is also small Meanwhile the SNRvalue of the ltered ECG is high indicating that the algo-rithm works for the BW interference suppression

As can be seen from Table 2 the eect of MMF issignicantly better than that of WT in the BW suppressione reason is that the frequency range of the Twave in ECGsignal is partially overlapped with the frequency range of BWnoise When the high-scale approximate components ofwavelet decomposition are set to zero wavelet re-construction could cause Twave distortion e CA gets thesmallest MSE and highest SNR which demonstrates that theperformance of BW suppression is better

4 Statistical Analysis

To further perform evaluation of CA a statistical analysisscheme is considered [17] Other two baseline removal al-gorithms used regularly in literatures which are Butterworth

Table 2 Frequency ranges of the estimated BW signal de-composition with seven scales

Wavelet coecients Frequency ranges (Hz)D1 90ndash180D2 45ndash90D3 225ndash45D4 113ndash225D5 56ndash113D6 28ndash56D7 14ndash28A7 0ndash14

ECG withoutBWsum

Estimated BWby MMF

ECG contaminatedBW

Waveletdecomposition

Reserving higherscale components

Waveletreconstruction

SmoothedBW

Smoothing BW by WT

ndash+

Figure 2 Block diagram of the CA

0 1 2 3 4 5 6 7 8 9 10ndash2

0

2

Time (s)m

V

(a)

0 1 2 3 4 5 6 7 8 9 10Time (s)

ndash2

0

2

mV

(b)

0 1 2 3 4 5 6 7 8 9 10Time (s)

ndash1

ndash05

0

mV

(c)

Figure 1 Example of removing BW using morphology lter (a) e ECG contaminated by BW (b) e ltered ECG signal by MMF (c)e estimated BW


high-pass lter [18] and wavelet-based high-pass ltering[19] are introduced and compared

e original articial ECG signals for this experimentare generated using the ECGSYM software [20] whichallows conguring ECG parameters (such as heart ratesampling frequency the morphology of the ECG wavesamplitude and duration parameters etc) For the experi-ment four segments of articial ECG signals with dierentheart rates which are 40 beats per minute (bpm) (bra-dycardia) 70 bpm (normal) 90 bpm (tachycardia) and120 bpm (exercise) are generated respectively and thesampling frequency is set to 360Hz and duration of thesignal to 5min Afterwards the real baseline drifts from theMIT-BIH Noise Stress Test Database [21] are added to thearticial ECG

ree performance indexes are chosen to evaluatethe algorithms besides above MSE which are describedbelow

41 Correlation Coecient (CC) It is used to quantify im-pairment in the morphology of the ltered signals It isindependent from scaling or osetting the signals and fo-cuses on the matching form of original and ltered wave-forms [17] Mathematically the correlation coecientbetween the original signal x(t) and the ltered one x(t) isgiven by

CC x(t) x(t) E x(t)minus μx( ) x(t)minus μx( )[ ]

σxσx

(21)

where E[middot] denotes the expected value operator μx is theexpected value of x(t) and σx is its standard deviation

42 L_Operator (LO) It is a measurement of similarity thatis based on the Euclidian distance between the two signals[21] Mathematically it is given by

LO x(t) x(t) 1minusE (x(t)minus x(t))2[ ]

E x2(t)[ ] + E x2(t)[ ] (22)

In contrast to the correlation coecient the LO is sen-sitive to osetting and scaling of any of the two signals [17]

43 Absolute Maximum Distance (AMD) It is one of themost commonly similarity metrics used to determine thequality of ECG signals after performing a ltering processand can be dened by the following expression [22]

AMD x(t) x(t) max|x(t)minus x(t)| (1lemle r)

(23)

where m is the number of the current sample of the signalsand r is the maximum number of samples of the x(t) andx(t) signals

It allows to measure the accumulated error and givesdierences in all their extension

e average results of the comparison study are pre-sented in Table 4

e results demonstrated that even though there aresmall dierences among the methods they were all goodperformers in terms of CC LO AMD and MSE Howeverwe see that the method that best maintained the original

0 1 2 3 4 5 6 7 8 9 10Time (s)

ndash2

0

2

4

Vol

tage

(mV

)

Figure 3 Articial ECG signal

0 1 2 3 4 5 6 7 8 9 10Time (s)

Vol

tage

(mV

)

ndash05

0

05

1

Figure 4 e chosen BW

Table 3 Values of the MSE and SNR

Signal MSE SNRArticial ECG 01170 30757ECG ltered by WT 00173 89145ECG ltered by MMF 00051 135224ECG ltered by CA 00024 167154


ECG morphology is CA (highest CC and LO and lowestAMD and MSE) e reason for this is probably due to thecombination of MMF and WT whose features match pre-cisely the time and frequency domain properties of theartifact

e second best performance according to the indexesis yielded by the WT method It is probably due to theproperties of the chosen suited wavelet and the relativelyhigh decomposition level Although wavelet-based high-passfiltering method is very similar to the wavelet-based methoda high-pass filtering (an infinite impulse response filter oforder one and a cutoff frequency of 05Hz) is used on theapproximation coefficients instead of setting them to zerois is somewhat comparable to a soft threshold on theapproximation coefficients And the Vaidyanathan-Hoangwavelet not coif3 used in WT is used [17 19]

According to the indexes Butterworth (lowest CC andhighest MSE) andMMF (lowest LO and highest AMD) showa similar worst performance Even so computationallyButterworth can be approximated as a finite impulse re-sponse filter and MMF significantly reduces the amount ofcomputation by opening and closing operators ey bothhave speedy computation and especially suit for medicalapplications that require fast but still accurate signal pro-cessing algorithms

5 Conclusion

In presence of baseline wanders there is a need to use apromising technique for baseline drifts suppression In thispaper we have presented and validated a combined algo-rithm of mathematical morphology filter and wavelettransform for baseline wandered ECG signals Comparedwith the current state-of-the-art methods the filtering effectof the presented algorithm is better and it can effectivelyfilter out the BW in the ECG signal meanwhile keeping thedistortion of the ECG signal minimized (the smallest MSEand highest SNR) is gives the opportunity to study verylow amplitude complexes and therefore it is suited for thedata preprocessing for precise ECG characteristic extraction

Data Availability

e ECG data used to support the findings of this study havebeen deposited in the MIT-BIH arrhythmia database(httpsdoiorgdoi1013026C2F305)

Conflicts of Interest

e authors declare that they have no conflicts of interest

Authorsrsquo Contributions

Xiang-kui Wan and Fei Qiao contributed to the conceptionof the study Fei Qiao Feng-cong Li and Haibo Wu con-tributed significantly to analysis and manuscript prepara-tion Xiang-kui Wan Feng-cong Li and Fei Qiao performedthe data analyses and wrote the manuscript and Yan LiYue-wen Yan and Jia-xin Wei helped perform the analysiswith constructive discussions

Acknowledgments

is work was supported by the National Nature ScienceFoundation of China (no 61571182) and the ResearchFoundation for Talented Scholars of Hubei University ofTechnology (no BSQD14033)

References

[1] J Q Li G Q Deng W Wei et al ldquoDesign of a real-time ECGfilter for portable mobile medical systemsrdquo IEEE Access vol 5pp 696ndash704 1998

[2] T Y Ji Z Lu Q H Wu and Z Ji ldquoBaseline normalisation ofECG signals using empirical mode decomposition andmathematical morphologyrdquo Electronics Letters vol 44 no 2pp 82-83 2008

[3] R F von Borries J H Pierluissi and H Nazeran ldquoWavelettransform-based ECG baseline drift removal for body surfacepotential mappingrdquo in Proceedings of 27th Annual In-ternational Conference of the Engineering in Medicine andBiology Society pp 3891ndash3894 Shanghai China September2005

[4] Y J Li H Yan and Z L Wang ldquoA comparative study on themethods of ECG baseline drifts removalrdquo Space Medicine ampMedical Engineering vol 5 pp 381ndash386 2009

[5] H Ji J X Sun and L Mao ldquoAn adaptive filtering algorithmbased on wavelet transform and morphological operation forECG signalsrdquo Signal Processing vol 22 no 3 pp 333ndash3372006

[6] S A Taouli and F Bereksi-Reguig ldquoNoise and baselinewandering suppression of ECG signals by morphologicalfilterrdquo Journal of Medical Engineering amp Technology vol 34no 2 pp 87ndash96 2009

[7] Q Zhao J Zhao and L Wei ldquoECG signal denoising algo-rithm based on wavelet transformrdquo Progress in ModernBiomedicine vol 10 pp 1566ndash1568 2007

[8] S Omid and BM Shamsollahi ldquoMultiadaptive bionic wavelettransform application to ECG denoising and baseline wan-dering reductionrdquo EURASIP Journal on Advances in SignalProcessing vol 2007 pp 1ndash11 2007

[9] J Z Song H L Yan L Yan and K Y Mu ldquoResearch onelectrocardiogram baseline wandering correction based onwavelet transform QRS barycenter fitting and regionalmethodrdquo Australasian Physical amp Engineering Sciences inMedicine vol 33 no 3 pp 279ndash283 2010

[10] L F Brown and S P Arunachalam ldquoReal-time T-p knotalgorithm for baseline wander noise removal from the elec-trocardiogramrdquo Biomedical Sciences Instrumentation vol 45pp 65ndash75 2009

[11] Y Sun K L Chan and S M Krishnan ldquoECG signal con-ditioning by morphological filteringrdquo Computers in Biologyand Medicine vol 32 no 6 pp 465ndash479 2002

Table 4 e average results

Methodsindexes CC LO AMD (mV) MSEButterworth 09742 09718 102 00128Wavelet high-pass 09801 09826 499 00096WT 09895 09890 410 00072MMF 09791 09705 1591 00109CA 09937 09929 259 00049


[12] Y Pang L Deng and J Z Lin ldquoECG signal removal based onmorphological filtering for baseline driftrdquoActa Physica Sinicavol 9 pp 428ndash433 2014

[13] G Chen M H Tang and H Chen ldquoECG signal denoisingalgorithm based on morphology and wavelet transformrdquoComputer Technology and Development vol 2 pp 100ndash1022012

[14] G B Moody and R G Mark ldquoe MIT-BIH arrhythmiadatabase on CD-ROM and software for use with itrdquo Com-puters in Cardiology vol 17 pp 185ndash188 1990

[15] X Wan Y Li C Xia M Wu J Liang and N Wang ldquoAT-wave alternans assessment method based on least squarescurve fitting techniquerdquo Measurement vol 86 pp 93ndash1002016

[16] G B Moody W Muldrow and R G Mark ldquoA noise stresstest for arrhythmia detectorsrdquo Computers in Cardiologyvol 11 pp 381ndash384 1984

[17] G Lenis N Pilia A Loewe W H W Schulze and O DosselldquoComparison of baseline wander removal techniques con-sidering the preservation of STchanges in the ischemic ECG asimulation studyrdquo Computational andMathematical Methodsin Medicine vol 2017 Article ID 9295029 13 pages 2017

[18] M S Chavan R A Agarwala and M D Uplane ldquoSup-pression of baseline wander and power line interference inECG using digital IIR filterrdquo International Journal of CircuitsSystems And Signal Processing vol 2 no 2 pp 356ndash365 2008

[19] K L Park K J Lee and H R Yoon ldquoApplication of a waveletadaptive filter to minimise distortion of the ST-segmentrdquoMedical and Biological Engineering and Computing vol 36no 5 pp 581ndash586 1998

[20] A L Goldberger L Amaral L Glass J M Hausdorff et alldquoPhysioBank PhysioToolkit and PhysioNet components of anew Research resource for complex physiologic signalsrdquoCirculation vol 101 no 23 pp 215ndash220 2000

[21] G Lenis Y Lutz G Seeman et al ldquoPost extrasystolic T wavechange in subjects with structural healthy ventricles-measurement and simulationrdquo in Proceedings of 41st Com-puting in Cardiology Conference pp 1069ndash1072 IEEECambridge Mass USA September 2014

[22] R Nygaard G Melnikov and A K Katsaggelos ldquoA ratedistortion optimal ECG coding algorithmrdquo IEEE Transactionson Biomedical Engineering vol 48 no 1 pp 28ndash40 2001


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sequences [11 12] However its applications may result inldquostep-likerdquo waveform distortions Wavelet transform(WT) has also been used in BW removal In [3] BW isestimated from the discrete WTcoefficients at level j and issubtracted from the original ECG signals WT methodexhibits relatively good effects for BW suppressionHowever this method causes T waveform distortions dueto the frequency overlaps between the high-scale ap-proximate coefficients and T wave e ECG signal isreconstructed by an inverse WT and the high-scale ap-proximate coefficients are set to zero thereby causing theT wave distortion [13]

is study introduces a combined algorithm (CA) ofMMF- and WT-based filtering for BW suppression e CAcan effectively preserve the outline of the BW and avoidwaveform distortions caused by morphology filters therebyobtaining an enhanced ECG quality

e study is organized as follows Section 2 describes thecombined filtering method while the simulation results areprovided and quantitatively analyzed in Section 3 Finallysummary and conclusions are drawn in Section 4

2 The Combined Method

Considering that the main focus of this study is BW sup-pression we model the contaminated ECG as the super-position of the real ECG and the BW and ignoring othertypes of interferences as follows

fCECG(n) fECG(n) + fBW(n) (1)

where fCECG fECG and fBW are the contaminated ECG-real ECG- and BW-function with respect to time index nrespectively All of the time functions in this study arediscrete because the implementation of filtering is focusedon digital processing e BW suppression is commonlyimplemented by cancellation ie

1113954fECG(n) fCECG(n)minus 1113954fBW(n) (2)

where the hat symbol 1113954 denotes the estimation of the un-derneath term e output error of this cancellation pro-cedure is given by

e(n) fECG(n)minus 1113954fECG(n) 1113954fBW(n)minusfBW(n) (3)

which indicates that the performance of BW suppression isdetermined by the estimator of fBW ie 1113954fBW To refine theestimator 1113954fBW we provide a staged framework whichcombines N different filtering technology e expression ofthis framework is shown as follows

1113954fBW(n) fF1 middot fF2 middot middot fFN( 1113857 fCECG(n)( 1113857 (4)

where fFn is the nth filter and operator middot denotes functioncomposition defined as follows

(f middot g)(x) f(g(x)) (5)

By choosing filters carefully the framework is capable ofcombining advantages of different filter implementationsand in this study we combine the MMF-based filter andWT-based filter

21 7e Morphological Filtering e shortcomings of thelinear BW suppression methods are caused by the nonlinearnature of the contaminated ECG Hence nonlinear pro-cessing methods are preferred and the MMF belongs to thiscategory which is capable of maintaining the shape of theinput signale objects of the morphological operations aresets and vectors for the clarity of descriptions hereaftervectors are denoted by lower case boldface letters and RN

denotes the real coordinate space of N dimensions ereflection of a set comprised of vectors is defined as

Ar

minusa ∣ a isin A (6)

while the translation is given by(A)z a + z ∣ a isin A (7)

and hence the dilation and erosion can be expressed asfollows

AoplusB z ∣ Br

( 1113857z capAneempty1113864 1113865

A⊖B z ∣(B)z subeA1113864 1113865(8)

e morphological filter is comprised of opening andclosing operators which can be expressed by dilation anderosion as follows

AB (A⊖B)oplusB (9)

A bullB (AoplusB)⊖B (10)

We can apply these morphological operators to a timefunction by treating the nminusf plane as a binary image andthe value of the pixels underneath the curve equals one egeometric interpretation of opening in equation (9) andclosing in equation (10) is sliding a given structuring elementalong with the signal from beneath and above respectivelySpecifically the result of opening comprises the highestpoints reached by any part of the structuring element whileclosing is comprised of the lowest ones Consequently thesemantic meaning of openingclosing is peak-suppressionpit-filling According to themodel shown in equation (1) thespiky fECG can be seen as the noise for fBW estimation andintuitively the combination of opening and closing is capableof smoothing the fluctuation introduced by the fECG eexpression of the estimator has the following form

fMMF fCECG( 1113857 12

fCECG S bull S( 1113857 + fCECG bull S S( 11138571113858 1113859

(11)

where S is the structuring element Let the output of the filterbe the estimation of fBW ie

1113954fBW fMMF fCECG( 1113857 (12)

the estimation of fECG can be obtained by cancellation1113954fECG fCECG minus 1113954fBW IminusfMMF( 1113857 fCECG( 1113857 (13)

where I denotes the identity operator ieI(f) f (14)

We test the estimator and the cancellation procedureusing Massachusetts Institute of Technology-Bostonrsquos Beth

















fECG(n) 1113944m

fSHB(n + mT) (17)









MSE 1N

sum

Nminus1


2 (18)

SNR 10 times lgθ2

MSE( ) (19)


θ2 1N

sum

Nminus1


2 (20)








ECG withoutBWsum

Estimated BWby MMF

ECG contaminatedBW




SmoothedBW

Smoothing BW by WT

ndash+


0 1 2 3 4 5 6 7 8 9 10ndash2

0

2

Time (s)m

V

(a)

0 1 2 3 4 5 6 7 8 9 10Time (s)

ndash2

0

2

mV

(b)

0 1 2 3 4 5 6 7 8 9 10Time (s)

ndash1

ndash05

0

mV

(c)








σxσx

(21)




E x2(t)[ ] + E x2(t)[ ] (22)




(23)





0 1 2 3 4 5 6 7 8 9 10Time (s)

ndash2

0

2

4

Vol

tage

(mV

)


0 1 2 3 4 5 6 7 8 9 10Time (s)

Vol

tage

(mV

)

ndash05

0

05

1








5 Conclusion


Data Availability






Acknowledgments


References































of




Disease Markers



OncologyJournal of





PPAR Research



Volume 2018


Journal of

ObesityJournal of


































fECG(n) 1113944m

fSHB(n + mT) (17)









MSE 1N

sum

Nminus1


2 (18)

SNR 10 times lgθ2

MSE( ) (19)


θ2 1N

sum

Nminus1


2 (20)








ECG withoutBWsum

Estimated BWby MMF

ECG contaminatedBW




SmoothedBW

Smoothing BW by WT

ndash+


0 1 2 3 4 5 6 7 8 9 10ndash2

0

2

Time (s)m

V

(a)

0 1 2 3 4 5 6 7 8 9 10Time (s)

ndash2

0

2

mV

(b)

0 1 2 3 4 5 6 7 8 9 10Time (s)

ndash1

ndash05

0

mV

(c)








σxσx

(21)




E x2(t)[ ] + E x2(t)[ ] (22)




(23)





0 1 2 3 4 5 6 7 8 9 10Time (s)

ndash2

0

2

4

Vol

tage

(mV

)


0 1 2 3 4 5 6 7 8 9 10Time (s)

Vol

tage

(mV

)

ndash05

0

05

1








5 Conclusion


Data Availability






Acknowledgments


References































of




Disease Markers



OncologyJournal of





PPAR Research



Volume 2018


Journal of

ObesityJournal of



















MSE 1N

sum

Nminus1


2 (18)

SNR 10 times lgθ2

MSE( ) (19)


θ2 1N

sum

Nminus1


2 (20)








ECG withoutBWsum

Estimated BWby MMF

ECG contaminatedBW




SmoothedBW

Smoothing BW by WT

ndash+


0 1 2 3 4 5 6 7 8 9 10ndash2

0

2

Time (s)m

V

(a)

0 1 2 3 4 5 6 7 8 9 10Time (s)

ndash2

0

2

mV

(b)

0 1 2 3 4 5 6 7 8 9 10Time (s)

ndash1

ndash05

0

mV

(c)








σxσx

(21)




E x2(t)[ ] + E x2(t)[ ] (22)




(23)





0 1 2 3 4 5 6 7 8 9 10Time (s)

ndash2

0

2

4

Vol

tage

(mV

)


0 1 2 3 4 5 6 7 8 9 10Time (s)

Vol

tage

(mV

)

ndash05

0

05

1








5 Conclusion


Data Availability






Acknowledgments


References































of




Disease Markers



OncologyJournal of





PPAR Research



Volume 2018


Journal of

ObesityJournal of
























σxσx

(21)




E x2(t)[ ] + E x2(t)[ ] (22)




(23)





0 1 2 3 4 5 6 7 8 9 10Time (s)

ndash2

0

2

4

Vol

tage

(mV

)


0 1 2 3 4 5 6 7 8 9 10Time (s)

Vol

tage

(mV

)

ndash05

0

05

1








5 Conclusion


Data Availability






Acknowledgments


References































of




Disease Markers



OncologyJournal of





PPAR Research



Volume 2018


Journal of

ObesityJournal of






















5 Conclusion


Data Availability






Acknowledgments


References































of




Disease Markers



OncologyJournal of





PPAR Research



Volume 2018


Journal of

ObesityJournal of



































of




Disease Markers



OncologyJournal of





PPAR Research



Volume 2018


Journal of

ObesityJournal of



















electrocardiogrambaselinewandersuppressionbasedonthe ...eprints.usq.edu.au/36130/1/wan...

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