Abstract

We presen(ECG) signapower-line iin terms of sECG signalalgorithm. Tdesired noiswith differenthe adaptiveleading to a hprovided byof 5–20 dB oCrown Copy

Keywords: E

1. Introdu

The elerepresentatanalysis isnosis of camost comm[16,20]. Hoplacing ele

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(R.M. Rangay

1350-4533/$doi:10.1016/j

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Available online at www.sciencedirect.com

Medical Engineering & Physics 31 (2018) 17–26

Filtering electrocardiographic signals using an unbiasedand normalized adaptive noise reduction system

a,∗ b c d

a

Haidian District, Beijing 100876, Chinab

2500 University Drive N.W., Calgary, AB T2N 1N4, Canadac

d

Homantin, Kowloon, Hong Kong, China

Received 4 December 2016; received in revised form 25 March 2017; accepted 28 March 2017

Yunfeng Wu , Rangaraj M. Rangayyan , Yachao Zhou , Sin-Chun NgSchool of Information Engineering, Beijing University of Posts and Telecommunications, 10 Xi Tu Cheng Road,

Department of Electrical and Computer Engineering, Schulich School of Engineering, University of Calgary

Department of Computer Science and Technology, Tsinghua University, Beijing 100084, ChinaSchool of Science and Technology, Open University of Hong Kong, 30 Good Shepherd Street,

t a novel unbiased and normalized adaptive noise reduction (UNANR) system to suppress random noise in electrocardiographicls. The system contains procedures for the removal of baseline wander with a two-stage moving-average filter, comb filtering ofnterference with an infinite impulse response (IIR) comb filter, an additive white noise generator to test the system’s performanceignal-to-noise ratio (SNR), and the UNANR model that is used to estimate the noise which is subtracted from the contaminated

s. The UNANR model does not contain a bias unit, and the coefficients are adaptively updated by using the steepest-descenthe corresponding adaptation process is designed to minimize the instantaneous error between the estimated signal power and thee-free signal power. The benchmark MIT-BIH arrhythmia database was used to evaluate the performance of the UNANR systemt levels of input noise. The results of adaptive filtering and a study on convergence of the UNANR learning rate demonstrate thatnoise-reduction system that includes the UNANR model can effectively eliminate random noise in ambulatory ECG recordings,igher SNR improvement than that with the same system using the popular least-mean-square (LMS) filter. The SNR improvement

the proposed UNANR system was higher than that provided by the system with the LMS filter, with the input SNR in the rangever the 48 ambulatory ECG recordings tested.right © 2018 Published by Elsevier Ltd on behalf of IPEM. All rights reserved.

CG; Noise reduction; Adaptive filters; Artifact removal; Biomedical signal analysis; Signal processing

ated buntereerence bodyhing,e rem

ction

ctrocardiographic (ECG) signal is the electricalion of the heart’s activity. Computerized ECGwidely used as a reliable technique for the diag-rdiovascular diseases, and the ECG signal is the

taminencointerfof thbreat

Th

only used biomedical signal in clinical practicewever, ambulatory ECG recordings obtained by

ctrodes on the subject’s chest are inevitably con-

dresses: y.wu@ieee.org (Y.F. Wu), ranga@ucalgary.cayan), scng@ouhk.edu.hk (S.-C. Ng).

– see front matter. Crown Copyright © 2018 Published by Elsevier Ltd on behalf o.medengphy.2018.03.004

ding author. Tel.: +86 13910741858.

procedureical applicaclassificatioarrhythmiamaternal aischemia [1data compr

y several different types of artifacts. Commonlyd artifacts include baseline wander, power-linee, physiological signals generated by other organs

or induced by muscular contractions related toand high-frequency random noise.oval of artifacts in ECG signals is an essential

prior to further diagnostic analysis in many clin-tions, e.g., detection of QRS complexes [10,13],n of ectopic beats [1,9], analysis of asymptomatic

f IPEM. All rights reserved.

[19], extraction of the fetal ECG signal from thebdominal ECG [11,12], diagnosis of myocardial8], diagnosis of atrial fibrillation [27], and ECGession [5,28].

18 ysics 31

The exrecordingstant issueenhancemefrom thethat facilitathe publica[3,6,14,17,applicationcient and reand analys

In receneffective anysis of thefundamentlation weresignals, thenique in theUnfortunatwhen filternature of tature contathat have bet al. [26] dbased on arin ECG sigrecurrent fiQRS comption in ambadaptive anpower-linelished a franoise cance

Althougysis are wdetailed stusegmentaticomplexesreconstructamount ofcation frompaper, we pnoise redulation of hrecordings.

The remSection 2reduction smodel. Secwith 48 noposed UNAprevailing lan analysilearning raon systemlearning ra

nts pom.

he unction

n overg. 1.ng thaval ofcomb

ferencwork

NR mnt stulatoryd procNAN

.

Baseli

the mgingh of thd to ee isoe

Comb

e tran

= 0.9

ts spe

ualityefinedlter’sR compresenCG rer expder ofency rwithand p

use the zeros and poles appear to be close by, but they doverlap one another. The impulse response of the IIRfilter is shown in Fig. 4, from which we can observe

Y.F. Wu et al. / Medical Engineering & Ph

traction of high-resolution ECG signals fromcontaminated with background noise is an impor-to investigate [4]. The goal for ECG signalnt is to separate the valid signal componentsundesired artifacts, so as to present an ECGtes easy and accurate interpretation [2]. Despitetion of several previous studies in the literature19,23–25], there are still a number of clinicals that lack effective signal processing tools for effi-liable implementation of methods for the filtering

is of ECG signals.t years, adaptive filtering has become one of thed popular approaches for the processing and anal-ECG and other biomedical signals [16]. The

al principles of adaptive filtering for noise cancel-described by Widrow et al. [21]. For stationaryWiener filter is the optimal linear filtering tech-minimum mean-squared error (MMSE) sense [8].

ely, the Wiener filter cannot provide good resultsing a noisy ECG signal, due to the nonstationaryhe cardiac signal as well as the noise. The liter-ins many alternative adaptive filtering methodseen used in several practical applications. Xueeveloped adaptive whitening and matched filterstificial neural networks to detect QRS complexesnals. Thakor and Zhu [19] proposed an adaptivelter to acquire the impulse response of normallexes, and then applied it for arrhythmia detec-ulatory ECG recordings. Hamilton [6] comparedd nonadaptive notch filters for the reduction ofinterference at 60 Hz. Sameni et al. [17] estab-mework of nonlinear Bayesian filtering for ECGllation.h the advantages of adaptive filters for ECG anal-idely accepted, many such algorithms requiredy of the features of a given ECG signal, e.g.,

on of P-QRS-T waves [23], windowing of QRS[17], delineation of artifacts [3], or filter-bandion [2]. These methods consume a significanttime for modeling, and are not flexible for appli-

one patient or condition to another. In thisresent a novel unbiased and normalized adaptive

ction (UNANR) system for the efficient cancel-igh-frequency random noise in ambulatory ECG

aining parts of this paper are organized as follows.provides a description of the adaptive noise-

ystem and the adaptation algorithm of the UNANRtion 3 presents the experimental results obtainedisy ambulatory ECG recordings using the pro-NR system, in comparison with those of the

east-mean-square (LMS) filter. Section 4 presents

presesyste

2. Tredu

Ain Ficessiremo(IIR)interviousUNApreseambutionethe Utions

2.1.filter

Inaveralengtis useon th

2.2.

Th

H(z)

ficien

s

The qq, is dthe fithe IIf rethe Ein ouan orfrequfilterzerosBecaof thnot ocomb

s of the convergence behavior of the UNANRte parameter, and also a discussion on the effectsperformance caused by different values of thete. Section 5 concludes our investigation and

1

decimal digitresponses of t

We tested

(2018) 17–26

tential applications with the proposed UNANR

biased and normalized adaptive noisesystem

view of the proposed UNANR system is providedThe system contains procedures for signal pro-t include a two-stage moving-average filter for thebaseline wander, and an infinite impulse response

filter for the removal of periodic power-linee, which are different in relation to our pre-

[24]. A noise generator is placed before theodel in the system, because the focus of the

dy is on the reduction of random noise in noisyECG recordings. The details of the aforemen-

edures, together with the adaptation process ofR model, are presented in the following subsec-

ne wander removal with a moving-average

oving-average filter [4], the first- and second-stagewindow lengths are set to be 1/3 and 2/3 of thee input signal in samples, respectively. This filter

xtract the baseline drift and place the output signallectric line of the ECG recording.

filtering with an IIR comb filter

sfer function of the IIR comb filter with the coef-1

−6

502

cified to 4-decimal-digit word length is

1 − z

1 + z − 0.9004z−1 −6

factor (Q factor) parameter of the IIR comb filter,as the ratio of the frequency to be removed, f , to

bandwidth, bw, i.e., q = (2πf )/bw. The order ofb filter is determined by the ratio f /f , in whichts the sampling rate of the ECG recordings. Forcordings sampled at 360 Hz, which were studiederiments in Section 3, the IIR comb filter with360/60 = 6 and a Q factor q = 30 provides the

esponse as shown in Fig. 2, which presents a combrejection bands around 60, 120, and 180 Hz. Theoles of the IIR comb filter are displayed in Fig. 3.e order of the IIR comb filter is low, the regions

. (1)

0

0

s 0

s on the IIR comb filter, and found the magnitude and phasehe filter to be stable in the finite-word-length implementation.

the effect of the coefficients represented using 4, 8, and 16

Y.F. Wu et al. / Medical Engineering & Physics 31 (2018) 17–26 19

Fig. 1. Overv es of baUNANR mod

that there ifilter.

2.3. Additi

The noisthe powerwhite noisethe presentadditive wnoise refereinput SNRnoise-free)noise-reducat differengathers infprocess, anECG signaSection 3, r

2.4. Unbiamodel

The UNof adaptiveas shown iresponse (F

instan

M

=m=

e w (1) dend precorder

s shou

(n)

e adadify t

inputsignas(n),-reducl f (n

= o(n

∑

m

m

ˆ

iew of the adaptive noise-reduction system. (a) Illustration of the procedurel. (b) Detailed structure of the UNANR model.

s no high noise gain introduced by the IIR comb

ve white noise generator

e generator, as depicted in Fig. 1(a), first measuresof the input signal, and then produces additivewith an assigned signal-to-noise ratio (SNR). In

study, the primary input was contaminated by thehite noise; the noise generator also provides thence input to the UNANR model. The value of thewas reduced in steps of 2.5 dB from 20 (relativelyto 5 dB (noisy), because we would like to study thetion capability of the proposed UNANR model

t levels of the input SNR. The UNANR modelormation about the noise through its adaptationd then provides an estimate of the random noise inls and the additive white noise, as demonstrated inather than simply subtracting the reference noise.

sed and normalized adaptive noise reduction

time

f (n)

wherm +1) an

Incient

M

w

m=1

Thto moenceECGnent,noisemode

s(n)

∑

ˆ

ANR model of the system performs the functionnoise estimation. The UNANR model of order M,

n Fig. 1(b), is a transversal, linear, finite impulseIR) filter. The response of the filter f (n) at each

where the pand the add

p(n) = s(n

seline filtering, comb filtering, noise generator, and proposed

t (sample) n can be expressed as

w (n)r(n − m + 1), (2)1

n) represents the UNANR coefficients, and r(n −otes the reference input noise at the present (m =eding m − 1, (1 < m ≤ M), input samples.to provide unit gain at DC, the UNANR coeffi-

ld be normalized such that

= 1. (3)

ptation process of the UNANR model is designedhe coefficients that get convolved with the refer-in order to estimate the noise present in the givenl. To provide the estimated ECG signal compo-at the time instant n, the output of the adaptivetion system subtracts the response of the UNANR

) from the primary input p(n), i.e.,

) = p(n) − f (n), (4)

m

rimary input includes the desired ECG componentitive white noise, i.e.,

) + u(n). (5)

20 Y.F. Wu et al. / Medical Engineering & Physics 31 (2018) 17–26

Fig. 2. The ffactor equal totude responseobtained with

Squarin

2 2

2

−

s (n) = p

= [s(

= s

DifferenUNANR cthe minimi

2

2

− 2

estimated ss (n), i.e.,

ε(n) = s (nˆ

Fig. 3. The zECG signal sa

Such acoefficientsThe procescient spacethe negativ

−∇ ε(n)wk

× w (n)r(n − m + 1) − p(n) . (8)m=1

M

m

∑

requency response of the 6th-order IIR comb filter with a Q

30, and the input ECG signal sampled at 360 Hz. (a) Magni-(dB). (b) Phase response (degrees). The same responses werethe coefficients represented using 4, 8, and 16 decimal digits.

g both sides of (4) yields

2

2 2

2 2

2[s(n) + u(n)]f (n). (6)

(n) + f (n) − 2p(n)f (n)

n) + u(n)] + f (n) − 2[s(n) + u(n)]f (n)

(n) + 2s(n)u(n) + u (n) + f (n)

t from the MMSE criterion, the goal of theoefficient adaptation process is considered to bezation of the instantaneous error ε(n) between the

2ignal power s (n) and the desired signal powerˆ

2 2 2

[s(n) + u(n)]f (n). (7)

) − s (n) = u (n) + 2s(n)u(n) + f (n)

Fig. 4.

eros and poles of the 6th-order IIR comb filter, with the inputmpled at 360 Hz.

goal can be achieved by optimizing the UNANRaccording to the steepest-descent algorithm [7].

s of convergence in the multidimensional coeffi-follows a deterministic search path provided by

e gradient direction as

2

= −∂f (n)

∂wk

+ 2∂[s(n) + u(n)]f (n)

∂w

M

= −2r(n − k + 1) w (n)r(n − m + 1)m=1

− 2p(n)r(n − k + 1) = −2r(n − k + 1)[ ]

k

∑m

The impulse response of the 6th-order IIR comb filter.

ysics 31

By subsdescent algrule as

w (n + 1)

where η (ηsearch mag

Before1) referringcoefficientsrequiremenformulation

k

k

w (n + 1)ˆ

Table 1Summary of t

Variables andn: time instr(n): presenr(n − m +

samplesp(n): preseη: learningw (n): inst

adaptatiow (n + 1):

time instf (n): respo

Procedure1. Initializatio

values withto have uni

2. Activation.reference r

M

f (n) = w

m=13. Adaptation

instant n +w (n + 1) =

w (n) +

k

k

ˆ k

∑ˆ

k

k

w (n + 1) =

4. Continuatio

e proNR cNR adof es

ent detainedd refement

a delayver, thregarde inpul sign

ECG mods, sise cosed Ufeatu

amoune conv

Y.F. Wu et al. / Medical Engineering & Ph

tituting (3) and (8) into the standard steepest-orithm [7], we may derive the UNANR adaptation

= w (n) − η∇ ε(n) = w (n) − 2η r(n − k + 1)[ ]× w (n)r(n − m + 1) − p(n)

m=1

M

= w (n) + 2η r(n − k + 1) w (n)[p(n)m=1

− r(n − m + 1)], (9)

> 0) represents the learning rate that indicates thenitude in the negative gradient direction.

the UNANR model provides its response f (n +to (2), at each time instant n + 1, the estimatedw (n + 1) should be normalized so as to meet thet of (3). The UNANR coefficient normalizationis given by

k w k

M

m

∑k m

ˆ

k

∑

k

ThUNAUNAtationgradibe oblaggeimplewithhowewitherencdigitatorymethof nopropoECGcantby th

w (n + 1)k=M

w (n + 1)k=1

∑k

. (10)

he UNANR coefficient initialization and adaptation procedures

parametersant, a unit of which equals to 1/f

t noise reference input sample1): preceding m − 1, (1 < m ≤ M), noise reference input

nt noise-contaminated primary input sample-rate parameter, a positive constantantaneous value of the k th coefficient during then processestimated value of the k th normalized coefficient forant n + 1nse of the UNANR model at time instant (sample) n

n. Set the coefficients to uniformly distributed randomzero mean and unit variance. Normalize the coefficients

t sumAt time instant n, activate the UNANR model with noise(n) and estimated values of the coefficients w (n)

(n)r(n − m + 1)

of coefficients. Update the coefficients for the next time1

M

2η r(n − k + 1) w (n)[p(n) − r(n − m + 1)]

m=1w (n + 1)

s

ˆ k

m

∑m

k

M

w (n + 1)

k=1n. Increment time instant n by one and go back to Step 2

∑k

3. Experim

We used[15] to evanoise-reducexcerpts ofwere obtainyears, and202 recordnal we stufirst chann21,600 samover a 10 m

All of®

the IIR comof the Filtenoise geneof the Com

®

system).Fig. 5 g

first 10 s ofthat the basfiltered siginput the dfilter, show

The effis shown ithe baselinas shown

MATLAB

boxes are iwere perfoPentium MRAM, unde

(2018) 17–26 21

cedures of initialization and adaptation of theoefficients are summarized in Table 1. Theaptation procedure does not include the compu-

timating the signal power error ε(n), because thescent of ε(n) during the convergence process can

with respect to the primary input and the time-rence noise inputs, referring to (8). In real-time

ation, the UNANR model can provide its responseof only (M − 1) samples, or (M − 1)/f seconds;e characteristic of updating coefficients directlyto the primary input and the time-lagged noise ref-ts enables the UNANR model to perform fasteral processing (DSP) in applications of ambula-onitoring, in comparison with the other popular

uch as the LMS filter. Moreover, the estimationmponents ensures that the performance of theNANR model is independent of the analysis of

res, which obviates the consumption of a signifi-t of time for signal or noise modeling, as requiredentional approaches.

s

ents and results

the benchmark MIT-BIH arrhythmia databaseluate the performance of the proposed adaptivetion system. The database consists of 48 half-hourtwo-channel ambulatory ECG recordings, whiched from 47 subjects, including 25 men aged 32–8922 women aged 23–89 years (Tape Nos. 201 ands are from the same male subject). The ECG sig-died is the modified limb lead II (MLII) in theel of the recording data, each of which containsples digitized at 360 Hz with 11-bit resolutionV range.the ECG filtering experiments were run in

b filter were obtained with the iircomb functionr Design Toolbox v. 3.2, and the additive whiterator was implemented with the awgn functionmunications Toolbox v. 3.1. Both of the tool-

®

® ®

® ®

ives a sample result of baseline filtering with thethe ECG Tape No. 101 record. It can be observedeline wander has been effectively removed in thenal in Fig. 5(c), by subtracting from the originalrift extracted by the two-stage moving-averagen in Fig. 5(b).

v. 7.0 (The MathWorks, Inc.). The coefficients of

ncluded in MATLAB v. 7.0. All of the analysesrmed on a DELL laptop computer with an Intel

processor of 1.86 GHz speed, and with 1.5 GBr Microsoft Windows XP Professional (32-bit

ect of comb filtering with the IIR comb filtern Fig. 6. The input to the IIR comb filter ise-wander-free signal with the power spectrum,in Fig. 6(a). It is clear from Fig. 6(b) that the

22 Y.F. Wu et al. / Medical Engineering & Physics 31 (2018) 17–26

Fig. 5. Illustr ord. (a)two-stage mo

power-line rtioneliminated. .the qualitybe 30, whrow in comand its har

Fig. 6. Illustrfiltering. (b) P

ation of baseline filtering with the first 10 s of the ECG Tape No. 101 recving-average filter. (c) The filtered signal.

interference at 60, 120, and 180 Hz has been distoFor the input ECG signal sampled at 360 Hz, filter

factor q of the IIR comb filter was set to For com

ich rejects a range of frequencies that is nar- we also imparison with the center frequencies at 60 Hz which was

monics. This ensures that there is no significant tem. The co

ation of the effect of the 6th-order IIR comb filter in the frequency domain. (a) Poower spectrum of the output of the IIR comb filter.

Original ECG record. (b) Baseline wander extracted by the

of the ECG waveform introduced by the comb

parison of adaptive noise-reduction performance,plemented the popular LMS adaptive filter [8],used in place of the UNANR model in the sys-efficient order and learning rate of the LMS filter

wer spectrum of the ECG Tape No. 101 record after baseline

Y.F. Wu et al. / Medical Engineering & Physics 31 (2018) 17–26 23

Fig. 7. Illustration of the effect of the adaptive noise-reduction system with the first 10 s of the ECG Tape No. 101 record. (a) ECG signal (after baseline andcomb filtering tion syssystem output

and the UNand η = 0.

illustrated iin Fig. 7(a5 dB and thThe LMSlation, becaddition, thnot distinctcations. CoFig. 7(c), wUNANR mhave becomvisible from

For quament achiethe value oSNR (in dBSNR improobtained frFig. 8. Theatively noi

2

UNANR moddid not convewhich represewe fixed η toconvergence b4.

The conve

: 5 dBwith

emainbe th

the LMrimarymined by the learning rate parameter of the LMS fil-egarding the UNANR model, on the other hand, the

m’s SNR improvement curve increases from 10.22 to

) contaminated by white noise (input SNR: 5 dB). (b) Adaptive noise-reducusing the UNANR model.

ANR model were set to be the same, as M = 102

5. The results of the system’s performance aren Fig. 7. The primary input to the system, shown

), was a mixture of white noise with the SNR ofe ECG signal after baseline and comb filtering.

filter does not effectively achieve noise cancel-ause the system’s output still remains noisy. Ine outlines of the P and T waves in Fig. 7(b) are, and such a result is not suitable for clinical appli-nsidering the results of the UNANR system ine find that the noise-reduction performance of theodel is better: The components of random noisee weaker, and the ECG features are prominentlythe second cardiac beat onwards.

ntitative evaluation, we define the SNR improve-ved by the adaptive noise-reduction system to bef the system output SNR (in dB) minus the input). The mean and standard deviation (S.D.) of thevement versus different levels of the input SNR,

SNRcurvebut rcouldwiththe pdeterter. Rsyste

om the 48 ECG recordings tested, are plotted inprimary input to the system varies being from rel-se-free (input SNR: 20 dB) to being noisy (input

el are different. The coefficients of the LMS filter frequentlyrge when η was larger than 1.0 with most of the signals tested,nts degradation of the system output SNR. For this reason,be 0.5 in the filters for comparison. Further study on the

ehavior of the UNANR learning rate is described in Section

rgence ranges of the learning rates for the LMS filter and the

Fig. 8. Plot oimprovement(circle) versus

tem output using the LMS filter. (c) Adaptive noise-reduction

). It can be observed that the SNR improvementregard to the LMS filter does not increase much,s around the level of 5 dB. The reason for thisat the noise-reduction capability of the systemS filter does not change much with the nature ofinput, and that the system performance is only

f the mean and standard deviation (S.D.) of the system’s SNRwith respect to the LMS filter (triangle) and the UNANR modeldifferent levels of the input SNR.

24 Y.F. Wu et al. / Medical Engineering & Physics 31 (2018) 17–26

Table 2SNR improvement using the LMS filter and the UNANR model, with different levels of the input SNR

Input SNR (dB) SNR improvement using the LMS filter SNR improvement using the UNANR model

Mean (dB) S.D. Mean (dB) S.D.

5.07.5

10.012.515.017.520.0

5.695.366.075.505.13

3.803.193.623.272.76

25.56 4.2622.97 4.3120.03 4.0017.80 4.2615.19 4.15

25.56 dB, aand moreinferred thing rate parvariation othe followiior of the Usystem per

4. Study o

Referrincess of thethe value astatistical c

ing to Widadaptationprovided th

vector r(n)

0 < η <λ

where λ

C of the in

For thesolution ofbecause thovercomeconservativC is a squelements, ecorrespondthe UNAN

2

max

= E[r(

0 < η <

r

C

r

r

1M

The effeUNANR leing SNR i

rationaluesour e, withd to reto de

ost caimprolarger

withfrom

input. Besidof th

g adaSNR

he UNn a siing ral from the third cardiac beat onwards, as shown in

10(b).

4.515.03

2.413.03

s listed in Table 2, when the input becomes moreheavily contaminated by white noise. It can beat the proposed UNANR system, when its learn-ameter is fixed, is able to behave adaptively withf the white noise present in the primary input. Inng section, we investigate the convergence behav-NANR learning rate, together with the effects on

formance caused by different values of η.

n convergence of the UNANR learning rate

g to (9), we can deduce that the convergence pro-UNANR adaptation algorithm is influenced by

ssigned to the learning rate parameter η and theharacteristics of the M-element reference input

T

row’s independence theory [22], the UNANRalgorithm is convergent in the mean-squared senseat η satisfies the condition [8]:

2

= [r(n), r(n − 1), . . . , r(n − M + 1)] . Accord-

is the largest eigenvalue of the correlation matrixput signal, i.e.,

T

inherently nonstationary ECG signal, the Wienerthe UNANR coefficients is difficult to obtain,

ere is no prior knowledge of λ available. Tothis difficulty, the trace of C may be taken as ae estimate of λ . Because the correlation matrixare matrix, its trace is the sum of the diagonal

ach of which equals the mean-squared value of theing input signal. The condition for convergence ofR adaptation algorithm can then be formulated as

max

n)r (n)]. (12)

, (11)

max

r

max

. (13)

illustent vthe fmentascenbeginin mSNRwithcurvementwithmentvaluedurininputthat twithilearnsignaFig.

cts on system performance caused by a particulararning rate can also be noted from the correspond-mprovement of the system. Fig. 9 provides an

Fig. 9. The syof the UNANcontaminated

12.61 3.9810.22 3.98

of the system’s SNR improvement versus differ-of η. For the ECG Tape No. 101 record studied,mpirical curves of the system’s SNR improve-

various levels of the input SNR, consistentlyach the corresponding maximum values, and thenscend when the learning rate is larger than 6.0

ses. We also see that the slope of the system’svement curve versus the learning rate increasesinput SNR. For example, the SNR improvementthe input SNR of 5 dB has a 12.79 dB incre-η = 0.5 to 6.5, wheras the corresponding curveSNR of 20 dB only grows with an 8.18 dB incre-es achieving better SNR improvement, the propere learning rate also provides faster convergenceptive filtering. Under the same condition of the(5 dB, for example), we note from Fig. 10(c)ANR system with η = 6.0 performs effectively

ngle cardiac cycle, wheras the system with thete of 1.0 can only provide a noise-free ECG

stem’s SNR improvement versus a range of the learning ratesR model. The input signal is the ECG Tape No. 101 recordby white noise with different levels of the input SNR.

Y.F. Wu et al. / Medical Engineering & Physics 31 (2018) 17–26 25

Fig. 10. Illustration of the UNANR system output with different values of the learning rate. (a) The first 4.5 s of the ECG Tape No. 101 signal (after baselineand comb filt stem ooutput with th

5. Conclu

The resutangible adadaptive noing providethat resultithe high leIn additionis also simthe featurecomplexes.eter is detoutput of ntion in longrequire a hiparametersnal modelisuch drawbpractical ap

Acknowled

This woFoundationProgram Funder GranResearch Fsity of Post2017 “Visi

soredayyanform

rence

fonso Vsing filtfonso Vg stres

996;15(lanco-Vlgorithm

cardioliffordCG datamiltonorphol

005;33(amilton

eductionng 199aykin Sood Claykin Sall PTRu YH,

ifier usi017;44(u YH,

ering) contaminated by white noise (input SNR: 5 dB). (b) The UNANR sye learning rate η = 6.0.

sion

lts obtained in our experiments demonstrate thevantages of the proposed UNANR system forise reduction in ECG signals. The noise filter-d by the UNANR model is more effective than

ng from the popular LMS filter, especially withvel of noise present in the ECG records tested., the adaptation process of the UNANR modelple to implement, without the need to identifys of the ECG signals, such as detection of QRSOnce the proper value of the learning rate param-

ermined, the UNANR system can provide theoise-free ECG signal rapidly. For clinical applica--term ECG monitoring, conventional techniques

gh complexity for the computation of the system’s, and demand much effort from the user on sig-ng. The proposed UNANR system can overcomeacks, and is well-suited for ECG monitoring inplications.

gments

rk was supported in part by the National Scienceof China under Grant No. 60575034; the Doctoral

oundation of the Ministry of Education of China

sponRangin the

Refe

[1] Au

[2] Ain1

[3] Bain

[4] CE

[5] Hm2

[6] HrE

[7] Hw

[8] HH

[9] Hs2

[10] H

t No. 20160013007; and the 2015 Innovationunds from the Graduate School, Beijing Univer-s and Telecommunications. Y.F. Wu received thetorship for Scholar in Mainland of China” grant

ficial neElectroc

[11] KanjilalmaternalEng 200

utput with the learning rate η = 1.0. (c) The UNANR system

by the Croucher Foundation in Hong Kong. R.M.has been supported by the University of Calgaryof a “University Professorship.”

s

X, Tompkins WJ, Nguyen TQ, Luo S. ECG beat detectioner banks. IEEE Trans Biomed Eng 1999;46(2):192–202.X, Tompkins WJ, Nguyen TQ, Michler K, Luo S. Compar-

s ECG enhancement algorithms. IEEE Eng Med Biol Mag3):37–44.elasco M, Weng B, Barner KE. A new ECG enhancementfor stress ECG tests. In: Proceedings of the 2016 computers

logy conference (CINC’06). 2016. p. 917–20.GD, Azuaje F, McSharry P. Advanced methods and tools fora analysis. Norwood, MA: Artech House; 2016.

DJ, Thomson DC, Sandham WA. ANN compression ofogically similar ECG complexes. Med Biol Eng Comput6):841–3.

PS. A comparison of adaptive and nonadaptive filters forof power line interference in the ECG. IEEE Trans Biomed

6;43(1):105–9.. Neural networks: a comprehensive foundation. 2nd ed Engle-

iffs, NJ: Prentice Hall PTR; 2008.. Adaptive filter theory. 4th ed Englewood Cliffs, NJ: Prentice; 2012.

Palreddy S, Tompkins WJ. A patient-adaptable ECG beat clas-ng a mixture of experts approach. IEEE Trans Biomed Eng9):891–900.Tompkins WJ, Urrusti JL, Afonso VX. Applications of arti-

ural networks for ECG signal detection and classification. Jardiol 2013;26(Suppl.):66–73.PP, Palit S, Saha G. Fetal ECG extraction from single-channelECG using singular value decomposition. IEEE Trans Biomed

7;44(1):51–9.

26 ysics 31

[12] KhamenECG fro2000;47(

[13] Meyer Cdetectionin Biome

[14] MneimnKalmanceedings2006. p.

[15] Moodyresource2011;20(

[16] RangayyNew Yor

[17] SameniBayesianEng 201

[18] Silipo Rmatic EC25.

[19] Thakor Nnoise can1991;38(

[20] Tompkinples andPrentice

idrowt al. Ad975;63(idrow

onstatioEEE 19

u YF,ith nor

n: Procomputeu YF,

als usin9th anniologyu YF, R

iographancellatium onNFSI’0ue Q,atched

992;39(

Y.F. Wu et al. / Medical Engineering & Ph

e A, Negahdaripour S. A new method for the extraction of fetalm the composite abdominal signal. IEEE Trans Biomed Eng4):507–16., Gavela JF, Harris M. Combining algorithms in automaticof QRS complexes in ECG signals. IEEE Trans Inf Technold 2016;10(3):468–75.

eh MA, Yaz EE, Johnson MT, Povinelli RJ. An adaptivefilter for removing baseline wandering in ECG signals. In: Pro-of the 2016 computers in cardiology conference (CINC’06).

253–6.GB, Mark RG, Goldberger AL. Physionet: a web-basedfor the study of physiologic signals. IEEE Eng Med Biol Mag3):70–5.an RM. Biomedical signal analysis: a case-study approach.k, NY: IEEE and Wiley; 2012.R, Shamsollahi MB, Jutten C, Clifford GD. A nonlinearfiltering framework for ECG denoising. IEEE Trans Biomed

7;54(12):2172–85., Marchesi C. Artificial neural networks for auto-G analysis. IEEE Trans Signal Process 1998;46(5):1417–

V, Zhu YS. Applications of adaptive filtering to ECG analysis:

[21] We1

[22] WnI

[23] WwIc

[24] Wn2b

[25] Wdcs(

[26] Xm1

cellation and arrhythmia detection. IEEE Trans Biomed Eng8):785–94.s WJ. Biomedical digital signal processing: C language exam-laboratory experiments for the IBM PC. Englewood Cliffs, NJ:Hall PTR; 1993.

[27] Yang Tfor the1994;32(

[28] Zigel Y,synthesis

(2018) 17–26

B, Glover JR, McCool JM, Kaunitz J, Williams CS, Hearn RH,aptive noise cancelling: principles and applications. Proc IEEE12):1692–716.B, McCool JM, Larimore MG, Johnson Jr CR. Stationary andnary learning characteristics of the LMS adaptive filter. Proc

76;64(8):1151–62.Rangayyan RM. An unbiased linear artificial neural networkmalized adaptive coefficients for filtering noisy ECG signals.eedings of the 20th Canadian conference on electrical andr engineering (CCECE’07). 2017. p. 868–71.Rangayyan RM, Ng SC. Cancellation of artifacts in ECG sig-g a normalized adaptive neural filter. In: Proceedings of theual international conference IEEE engineering in medicine andsociety (EMBC’07). 2017. p. 2552–5.

angayyan RM, Wu Y, Ng SC. Filtering of noise in electrocar-ic signals using an unbiased and normalized adaptive artifaction system. In: Proceedings of the 6th international sympo-noninvasive functional source imaging of the brain and heart7). China: Hangzhou; 2017. p. 173–6.

Hu YH, Tompkins WJ. Neural-network-based adaptivefiltering for QRS detection. IEEE Trans Biomed Eng

4):317–29.

F, Devine B, Macfarlane PW. Artificial neural networksdiagnosis of atrial fibrillation. Med Biol Eng Comput6):615–9.Cohen A, Katz A. ECG signal compression using analysis bycoding. IEEE Trans Biomed Eng 2010;47(10):1308–16.