Research Article A Hierarchical Method for Removal of ...downloads.hindawi.com/journals/tswj/2013/896056.pdfResearch Article A Hierarchical Method for Removal of Baseline Drift from

Hindawi Publishing CorporationThe Scientific World JournalVolume 2013 Article ID 896056 10 pageshttpdxdoiorg1011552013896056

Research ArticleA Hierarchical Method for Removal of Baseline Drift fromBiomedical Signals Application in ECG Analysis

Yurong Luo1 Rosalyn H Hargraves2 Ashwin Belle1 Ou Bai3 Xuguang Qi1

Kevin R Ward4 Michael Paul Pfaffenberger1 and Kayvan Najarian1

1 Department of Computer Science School of Engineering Virginia Commonwealth University 401 West Main StreetRichmond VA 23284 USA

2Department of Electrical and Computer Engineering School of Engineering Virginia Commonwealth University401 West Main Street Richmond VA 23284 USA

3Department of Biomedical Engineering School of Engineering Virginia Commonwealth University 401 West Main StreetRichmond VA 23284 USA

4Department of Emergency Medicine and Michigan Critical Injury and Illness Research Center University of MichiganAnn Arbor MI 48109 USA

Correspondence should be addressed to Ashwin Belle belleavcuedu

Received 12 February 2013 Accepted 9 April 2013

Academic Editors G Koch J Ma and V Positano

Copyright copy 2013 Yurong Luo et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Noise can compromise the extraction of some fundamental and important features from biomedical signals and hence prohibitaccurate analysis of these signals Baseline wander in electrocardiogram (ECG) signals is one such example which can be caused byfactors such as respiration variations in electrode impedance and excessive body movements Unless baseline wander is effectivelyremoved the accuracy of any feature extracted from the ECG such as timing and duration of the ST-segment is compromisedThispaper approaches this filtering task from a novel standpoint by assuming that the ECG baseline wander comes from an independentand unknown source The technique utilizes a hierarchical method including a blind source separation (BSS) step in particularindependent component analysis to eliminate the effect of the baselinewanderWe examine the specifics of the components causingthe baseline wander and the factors that affect the separation process Experimental results reveal the superiority of the proposedalgorithm in removing the baseline wander

1 Introduction

The electrocardiogram (ECG) is an important physiologicalsignal that helps determine the state of the cardiovascularsystem however this signal is often corrupted by interferingnoise Baseline wander is a commonly seen noise in ECGrecordings and can be caused by respiration changes inelectrode impedance and motion Baseline wander canmask important information from the ECG and if it is notproperly removed crucial diagnostic information containedin the ECG will be lost or corrupted Therefore it is vitalto effectively eliminate baseline wander before any furtherprocessing of ECG such as feature extraction

The simplestmethod of baseline wander (drift) removal isthe use of a high-pass filter that blocks the drift and passes all

main components of ECG though the filter The main com-ponents of ECG include the P-wave QRS-complex and T-wave Specifically the PR-Segment ST-Segment PR-Intervaland QT-Interval are considered as the main segments of theECG Each of these intervalssegments has its correspondingfrequency components and according to the AmericanHealth Association (AHA) the lowest frequency componentin the ECG signal is at about 005Hz [1] However a completebaseline removal requires that the cut-off frequency of thehigh-pass filter be set higher than the lowest frequency in theECG otherwise some of the baseline drift will pass throughthe filter The frequency of the baseline wander high-passfilter is usually set slightly below 05Hz Therefore knowingthat the actual ECG signal has components between 005Hzand 05Hz the forementioned simple approach for baseline

2 The Scientific World Journal

removal distorts and deforms the ECG signal In particu-lar it affects the ST-segment that has very low frequencycomponents Furthermore ectopic beats occurring in theECG during the course of different types of diseases andinjuries change the frequency spectrum of both the baselinewander and the ECG waveforms All the above-mentionedcharacteristics demand a more comprehensive approach thatworks for a wider range of applications and avoids distortingthe main ECG waves when removing the baseline drift

Digital filters are commonly employed method to elimi-nate baseline wander Cut-off frequency and phase responsecharacteristics are two main factors considered in the major-ity of these designsThe use of linear phase filters prevents theissue of phase distortion [2] For finite impulse response (FIR)filters it is rather straightforward to achieve linear phaseresponse directly Feed-forward and feed-back technologiessuch as infinite impulse response (IIR) filters can also provideminimum phase distortion [3] In all of these methods thecut-off frequency should be chosen so that the informationin the ECG signals remains undistorted while the baselinewander is removed which results in a trade-off Usually thecut-off frequency is set according to the slowest detected(or assumed) heart rate However if there are ectopic beatsin the ECG signal it is even more difficult to find thisparticular frequency It is a prevalent phenomenon that theoverlap between the baseline wander and low frequencycomponents of the ECG compromises the accuracy of theextracted features

Time-variant filters are designed to increase flexibility inthe adjustment and control of the cut-off frequency In suchmethods the cut-off frequency of the filter is controlled bythe low frequency characteristics of the ECG signal [4] Cubicspline curve fitting [5] linear spline curve fitting [6] andnonlinear spline curve fitting [7] belong to another family offilters that remove the baselinewander but often require somereference points For instance the linear spline curve fittingmethod [5] forms a subsignal of the ECG for a single cardiaccycle starting 60ms before the P-wave and ending 60ms afterthe T-wave and fits a first order polynomial to this sub-signalafter subtracting the mean of sub-signal Multirate systemwavelet transform has also been utilized for the ECG baselinewander removal The approach using wavelet adaptive filter(WAF) [8] consists of two steps First a wavelet transformdecomposes the ECG signal into seven frequency bands Thesecond step is an adaptive filter that uses the signal of theseventh lowest frequency band as the primary input and aconstant as a reference unit for filtering Another multi-ratesystem empirical mode decomposition (EMD) [9] has alsobeen adopted to eliminate the baseline wander Comparedwith the wavelet technique that uses some predefined basisfunctions to represent a signal EMD relies on a fully data-drivenmechanism that is EMDdoes not require any a-prioriknown basis

Adaptive filters as a cascade structure [10] have also beenused for this application The first step of this approach usesan adaptive notch filter to eliminate the DC component ofthe ECG The second step forms a comb filter assuming thatthe signal is an event-related signal Blind source separation(BSS) in particular independent component analysis (ICA)

[11ndash13] is another choice to remove the baseline wanderAs a specific type of BSS method ICA has been extensivelyused in biomedical signals [14ndash16] such as the ECG and theEEG It has been used as an effective method to decom-pose multichannel signals into fundamental componentsAs many more applications of ICA are being recognizednewer variations of ICA are being introduced Standard ICA[17] (sICA) is a technique that is used to estimate sourcesignals when several mixtures of signals are available Boththe source signals and the mixing process are unknown andthe sources are estimated only on the assumption that theyare statistically independent Comparing the formulation ofthe standard ICA convolutive ICA (fICA) deems that thefinite impulse response is closely associated with the mixingprocess and the mixing process can be considered as aweighted and delayed mixture of sources [18 19] Fast androbust fixed-point ICA [20] is produced based on the ideathat it is feasible to use contrast function to approximatenegentropy Through a fixed-point algorithm the contrastfunction is maximized to extract latent sources with highspeed Temporally constrained ICA [21 22] is a more flexiblemodel to separate latent sources By using prior knowledge oradditional constraints the targeted latent source is extractedMoreover there are many other forms of ICA for differentapplications such as topographic independent componentanalysis [23] and spatial and temporal independent compo-nent analysis [24]

In summary the traditional methods are limited in eitherfrequency delineation or reference choice and the case of BBSin applications mentioned previously does not give sufficientevidence in noise removal Based on these points of view inthe proposed method a unified method utilizing an adaptivenotch filter and BSS is used for baseline drift removal Specif-ically multichannel signals are constructed using a single-channel signal and ICA is applied to the ECG The maincontributions of our work lie in combining the capabilitiesof adaptive filters and BSS expanding the capabilities of theindependent components for this application by customizingthe ICA method towards the removal of the ECG baselinewander Furthermore the factors affecting the performanceof the separation process are explored and improved in thispaper

The rest of the paper is organized as follows The overallstructure of the proposed method is illustrated in Section 2The adaptive notch filter as employed in the paper isdescribed in Section 3 The concepts and formulation of theICA the fast and robust fixed-point ICA and the customizedform are introduced in Section 4 Section 5 introduces theprocess of detecting the components that cause the baselinewander and verifies this process This section also exploresthe factors that affect the separation of the results FinallySection 6 concludes the paper

2 Method

Figure 1 shows the framework of the proposed method As itcan be seen in Figure 1 the first step of the proposed methodis an adaptive notch filter designed to form subsignals ofthe ECG as described later Next as shown in Figure 1

The Scientific World Journal 3

ECG signal

Adaptive notch filter

Low frequency part of ECG signal

Construct

Old baseline wander

New baseline wander

Residual signal

Filtered ECG signal

Fast ICA

Adjust

Remove

Combine


High frequency part of ECG Signal

multichannel signal

Figure 1 Schematic diagram of proposed method

the proposed method utilizes ICA to remove the baselinedrift Considering the noisy nature of the typical raw ECGsignal in this study subsignals in low frequencies of the ECGare formed and these filtered signals are then formed byan adaptive notch filter then used as the input to the ICAalgorithmMoreover with regard to the inputs fed to the ICAalgorithm in this study only a single-channel ECG signal isavailableTherefore knowing that ICA requiresmultichannelsignals to process as its input in order to use ICA to removebaseline wander one needs to build multichannel signalsfrom the single-channel ECG In order to address this issuein the proposed method a systematic process was created inwhich delayed versions of the ECG are stacked to form themulti-channel signal In addition as shown in Figure 1 theindependent component formed by the ICA as the outputwhich is originally labeled as the baseline wander needsto be further adjusted to form a better estimate of thebaseline wander This is due to the fact that while one of thecomponents resembles the baseline drift it is unlikely that anyof the original components detected by the ICA is ldquopurelyrdquo thebaseline wander

The specific steps shown in Figure 1 are further describedbelow

(a) Form sub-signals of ECG using an adaptive notchfilter as shown in Figure 1 the adaptive notch filter[25 26] is designed and customized to form the sub-signal The reason for using the adaptive notch filteris its flexibility as well as its relatively superior per-formance compared with other filters As mentionedabove applying the ICA algorithm on a sub-signalof the ECG has the advantage of reducing the errors

coming from multi-channel signals in estimating thebaseline wander

(b) Construct multi-channel signals applying ICA re-quires that the signals are multi-channel ones How-ever in many ECG processing applications only thesingle-channel ECG signal is available andor pro-cessed The proposed method applies the method-ology in [11] to construct multi-channel signals bydelaying the single-channel signal In our study themulti-channel signals are constructed using sixtysignals which are delayed 10 sample points (sim83ms)of the original signal in succession

(c) Adjust the baseline wander extracted by ICA thebaseline wander extracted by ICA is an approxima-tion of the true baseline wander because (1) therewill be some errors in the resulting component dueto the fact that the estimation process used in theICA (in particular in the first few attempts) may benonoptimal (2) in the ICA analysis there may bemore than one maximum in the estimation functionand therefore the true baseline wander may not belocated accurately (3) the constructed multi-channelsignals cannot convey all information about the base-line wander and as such the proposed process mayalleviate the issues associated with the non-optimalconstruction of multi-channel signals The 10-sampleshift of the signals provides large enough variationsbetween the multisignal component to alleviate theissues concerning dependencies for ICA processing

3 Adaptive Notch Filter

The adaptive notch filter [26] is based on the same theoreticalfoundations as adaptive noise cancellation [25] There aretwo inputs in the structure of the adaptive noise cancellingOne is the primary input containing the signal and thenoise and the other one is the reference input which isthe reference signal related to the noise in the primaryinput Using least mean square (LMS) criterion the referencesignal is gradually approached to the noise in the primaryinput When the stability is achieved the output is acquiredthrough subtracting the reference input from the primaryinput This type of filter can deal with inputs that aredeterministic or stochastic stationary or time-variant If theinputs are stationary stochastic the solution of the adaptivenoise cancelling approaches closely Wiener filter [25] As tothe adaptive notch filter the reference signal is the signalwith one- or multifixed frequencies which are treated as thefrequencies to be excluded

The advantages of adaptive notch filters lie in the fol-lowing aspects (1) if the frequency of the interference is notprecisely known or the interference drifts in the frequencythe exact excluded frequency could be measuredadaptedduring the filtering process (2) the filter is tunable sincethe null point moves with the reference frequencies (3) theadaptive notch filter can be made very sharp at the referencefrequency (4) through adjusting the parameters the adaptivenotch filter can be considered as a time-invariant filter by


middot middot middot



middot middot middotmiddot middot middot


119889119896

sumsum + 119885minus1

1199101119896

119909119909

119910119873119896

119889119896120572

119910119894119896119908119894119896minus1119908119894119896minus1

120576119896

Figure 2 The diagram of adaptive noise cancelling

lessening the influence of the time-varying components Theinference of adaptive notch filter is described in [25 26] Thediagramof adaptive noise cancelling is shown in Figure 2Thesystem is an119873-stage tapped delay line (TDL) The weight ofthe filter is updated according to the following equations

119910119896 = 119908119879

119896119909119896

120576119896 = 119889119896 minus 119910119896

119908119896+1 = 119908119896 + 120597120576119896119909119896

(1)

where 119909 is the reference input 119889 is the desired response 119910 isthe output of the filter 119908 is the weight of the filter 120597 is theadaptation constant and 119896 is the time index As described in[26] the response from 119864(119911) to 119884(119911) includes two parts Inpractical applications it is feasible to make the time-varyingcomponent to be insignificant (120573119873 asymp 0) by changing thevalues of119873 and setting 120573 as follows

120573 =

sin (119873119908119903119879)sin (119908119903119879)

(2)

where119908119903 is the frequency of the interference If the referenceinput is considered to be the following form

119909 = 119862 cos (119908119903119879 + 120579) (3)

the transfer function of adaptive notch filter can be expressedas follows

119867(119911) =

119911

2minus 2119911 cos (119908119903119879) + 1

119911

2minus 2 (1 minus 119873120597119862

24) 119911 cos (119908119903119879) + (1 minus 11987312059711986222)

(4)

Therefore the parameter 119873 can be set to the fixed value asdescribed above It can be seen that the above-mentionedfilter is very flexible and can be adjusted using the adaptionconstants 120597 and 119862 to provide the desired bandwidth anddepth of a suitable notch filter

4 Independent Component Analysis

After applying the notch filter the main step used is ICAFirst the ldquostandardrdquo ICA is described ICA can be briefly

explained using a simple example of separating two sourcesignals 1199041(119905) and 1199042(119905) that were mixed by an unknown linearprocess Two different linear mixtures 1199091(119905) and 1199092(119905) aregiven as follows

1199091 (119905) = 119888111199041 + 119888121199042

1199092 (119905) = 119888211199041 + 119888221199042

(5)

where 11988811 11988812 11988821 and 11988822 are unknown coefficients Theobjective of the problem is to recover the signal 1199041(119905) and 1199042(119905)from mixture signals 1199091(119905) and 1199092(119905) without knowing anyprior information about the source signals 1199041(119905) and 1199042(119905) andthe mixing process (ie 11988811 11988812 11988821 and 11988822) except that 1199041(119905)and 1199042(119905) are statistically independent

In the generalized case where there are more latentsources and more mixture of signals the formal definition ofICA is as follows

119909119894 (119905) = 11988811989411199041 + 11988811989421199042 + sdot sdot sdot + 119888119894119899119904119899 119894 isin [1 119899] (6)

where 119904119894(119905) is called latent source 119909119894(119905) is the mixture signal119888119894119895 is the mixing coefficient between 119909119894(119905) and 119904119895(119905) and 119899 isthe number of latent sources and mixture signals The aboveformulation can be expressed as the following matrix form

119883 = 119862119899times119899 sdot 119878 (7)

where 119883 is the matrix of mixture signals in which eachcolumn is one mixture signal 119878 is the matrix of latent signalsin which each column is one latent signal and 119862119899times119899 is thematrix for mixing coefficients

The feasibility of solving the ICA problem lies in thecondition that the latent sources are independent of eachother According to the Central Limit Theorem the distribu-tion of a sum of independent random variables approachesa Gaussian distributionThis implies that the solution of ICAcan be achieved when distribution diverges fromGaussianityThe deviation from Gaussianity can be determined usingmeasures such as Negentropy

Negentropy is one measure of non-gaussianity definedbased on the concept of entropy which is the fundamentalconcept of information theory Entropy 119864 as a measure ofinformation in random variables is defined for a discreterandom variable 119910 as folows

119864 (119910) = minussum

119894

119875 (119910 = 119888119894) log119875 (119910 = 119888119894) (8)

where 119888119894 is the possible values of 119884 and 119875(119884 = 119888119894) means theprobability when the value of119884 is 119888119894 For a continuous randomvariable 119910 entropy 119864 is defined as the following equation

119864 (119910) = minusint119891 (119910) log (119891 (119910)) 119889119910 (9)

where 119891 is the probability distribution function Negentropy119869 is then defined as follows

119869 (119910) = 119864 (119910gauss) minus 119864 (119910) (10)


where 119910gauss is a Gaussian random variable with the samecovariance matrix as 119910 A fundamental conclusion in infor-mation theory is that a Gaussian variable has the largestentropy among all randomvariables of equal varianceHencenegentropy is always nonnegative and it is zero only if 119884 hasa Gaussian distribution

The exact calculation of negentropy requires an accurateestimation of the probability distribution function whichmay be computationally costly or data intensive There-fore it is often preferred to find simple approximations ofnegentropy Simple approximations of negentropy have beenintroduced [27] which are based on the maximum entropyprinciple In general the following family of approximationsis the most commonly used group

119869 (119910) =

119901

sum

119894=1

119896119894[119864 (119866119894 (119910)) minus 119864 (119866 (V))]2 (11)

where 119896119894 are constants and V is a gaussian random variablewith zeromean and unit variance Often the value of119901 and 119896119894can be set to one Therefore the above formulation becomesas follows

119869 (119910) = [119864 (119866 (119910)) minus 119864 (119866 (V))]2

(12)

The following formulations of 119866 functions have proved veryuseful in practical applications

1198661 (119910) =

1

1198861

log cosh (1198861119910) 1198921 (119910) = tanh (1198861119910)

1198662 (119910) = minus

1

1198862

exp(minus11988621199102

2

) 1198922 (119910) = 119910 exp(minus11988621199102

2

)

1198663 (119910) =

1

4

119910

4 1198923 (119910) = 119910

3

(13)

where 1 le 1198861 le 2 1198862 asymp 1 and 119892 is the first derivative of thefunction 119866

Before applying the main processing operations of theICA it is often necessary to perform some preprocessingUsually the two different operations are conducted centeringand whitening Centering requires that the random variable119910 is a zero-mean random variable and it is performed bysubtracting itsmean vectorWhiteningwill make the randomvariable uncorrelated and set their variances equal to unityby using the eigenvalue decomposition of their covariancematrix

119864 119910119910

119879 = 119863119881119863

119879 (14)

where119863 is the orthogonal matrix of eigenvectors and119881 is thediagonalmatrix of eigenvalues Now assuming that 119911 is a newrandom variable after whitening consider the following

119911 = 119863119881

minus12119863

119879119910 (15)

Whitening makes the problem change from estimating mix-ing matrix to estimating a new one 119862

119911 = 119863119881

12119863

119879119862119904 =

119862119904 (16)

Among several improvements of ICA fast and fixed-pointindependent component analysis [20] as a direct extensionof the standard ICA was developed for calculating latentsources with high speedThe basic rule of fast and fixed-pointindependent component analysis is to find a direction whichcan maximize non-Gaussianity of 119908119879119909 Non-Gaussianity isdecided according to the approximation of nongaussianity asmentioned aboveThe following is the basic description of thealgorithm

(a) Initialize a weight vector 119908 in one direction(b) Change the weight vector according to the following

criteria 1199081015840 = 119864119909119892(119908

119879119909) minus 119864119892

1015840(119908

119879119909)119908 and nor-

malize the weight vector as 119908 = 119908

1015840119908

1015840

(c) If the weights have not converged go back to step (b)

where 119908 is the weight vector to calculate latent source 119904 =119908

119879119909 and convergence means that the old weight vector and

the new weight vector are in the same directionIn this study the fast and fixed-point independent com-

ponent analysis [20] is used as the implementation of ICAblock shown in Figure 1

5 Results

An ECG dataset of human volunteer undergoing lower bodynegative pressure (LBNP) [28] as a surrogate of hemorrhagewas employed to verify the effectiveness of removing baselinewander This data set was created under Institutional ReviewBoard approval The LBNP dataset consisted of a total of 91subjects Each subject had a single vector lead ECG recordingcollected at the sampling rate of 500HzThe baseline wanderin ECG signals demonstrated significant level of variationsin the amplitude over the course of the LBNP experimentDuring LBNP subjects are exposed to increasing negativepressure to their lower bodies This causes a redistribution ofblood volume to the lower extremities and abdomen causinga decrease in blood pressure and cardiac output and resultingin an increased respiratory rate

The results of the proposed method are compared with areference method called robust locally weighted regression[29] which is often treated as one of the most robust andcommonly usedmethods to remove baseline driftThe robustlocally weighted regression method employs two techniquesthe local fitting of polynomials and an adaptation of iteratedweighted least squares to remove the baseline drift

51 Results of Adaptive Notch Filter One objective of theproposed system is the removal of unwanted frequenciesaround 0Hz as well as 60Hz As the frequencies around zeroare excluded the filter acts as a high-pass filter In order tolessen the influence of the time-varying components oneneeds to first set a suitable parameter119873 to obtain a desirablelevel of time-varying component 120573119873 Figure 3 shows thevalue of the time-varying component120573119873 for different valuesof119873

Figure 3 indicates that the value of 119873 determines thedegree at which the time varying component influences


0 002 004 006 008 01minus04

minus02

0

02

04

06

08

1

(a)

0 0002 0004 0006 0008 001 0012minus04

minus02

0

02

04

06

08

1

(b)

Figure 3 The resulting value of 120573119873 (a)119873 = 256 (b)119873 = 4096

0 50 100 150 200 2500

02040608

11214

Mag

nitu

de

Frequency (Hz)

(a)

0 50 100 150 200 2500

02040608

11214

Mag

nitu

de

Frequency (Hz)

(b)

Figure 4 Transfer function for two choices of adaptive notch filters (a) 119862 = 1 (b) 119862 = 001

0 50 100 150 200 2500

02

04

06

08

1

12

14

Mag

nitu

de

Frequency (Hz)

Figure 5 Transfer function of the adaptive notch filter around60Hz

the filter In general with the increase in the value of119873 thisinfluence decreases gradually In this study the value of119873wasset to 10000 The parameter 120597 identifies whether or not the

adaptation converges [25] The value of 120597 should be greaterthan 0 but less than the reciprocal of the largest eigenvalue120582 of the matrix 119877 which is defined as the correlation matrixof signal [25] In this study the value of 120597 was set to 00001The bandwidth of the filter can be approximated using thefollowing equation [26]

BW =

119873120597119862

2

2119879

(rads) (17)

Figure 4 shows the transfer function of the resultingadaptive notch filter and as expected this filter acts as a high-pass filterNote that the value of119862provides yet another degreeof freedom for this filter design process and hence Figure 4presents the transfer function for two different filters formedusing two different values of C each resulting in a verydifferent bandwidth A main advantage of the adaptive notchfilter used here is that changing the values of parameters 119873120597 and 119862 can provide a wide spectrum of desired filters withdiverse shapes of transfer function

Adaptive notch filter for frequencies around 60Hz isdesigned similarly The parameter119873 was to 2048 120597 to 0001and 119862 to 01 Figure 5 depicts the transfer function of theresulting adaptive notch filter


Table 1 Experimental results of removing the baseline wander

Subject Shiftelevation Error1

Error2

1 2900 20996 078472 2501 281832 270373 3004 1939524 344954 3001 243905 107275 3003 891358 362826 2902 179017 116147 3001 28955 106238 2000 1077542 1344399 3002 2038138 4084610 2902 817942 2281811 2902 2563747 8726412 3002 410977 2422313 2601 442238 227914 2602 1017592 2331715 3102 7001481 10142916 2901 127575 1352217 2901 456429 2641218 3100 368833 11822419 2901 91224 18820 2902 1813923 23019321 3002 254492 2642122 3704 2524353 8561623 2602 3047066 7463724 2901 1169048 37725 3001 163922 10526 2900 34748 0667127 3002 1444347 1857928 2900 239724 2164129 2901 145089 0220530 2901 1553859 3670731 3001 506959 2675732 3001 272665 110133 3001 567045 199934 2902 3244399 10031335 3001 426266 0879136 2902 5397357 31323837 2901 198874 0813138 2901 143623 2649939 2601 88582 6478740 3004 1350286 3005641 2901 295551 2754142 3001 433923 3005243 2900 510465 6924144 2900 319213 5464645 2901 97597 1332846 2701 227897 1359847 2902 935265 189948 2900 87422 1560749 3506 892829 74303450 3003 2094986 63436

Table 1 Continued

Subject Shiftelevation Error1 Error251 3003 605121 2664552 2901 37123 0948653 2904 2472271 513854 2501 320128 2860955 3100 201471 133656 3100 52858 4083957 2900 71664 0952658 3001 354656 0893259 2901 109895 0865360 3003 1157327 4838761 3001 267803 0714162 2902 93222 2880963 2901 169436 0946964 3000 277014 1779465 2901 551891 4922666 3106 6203234 8099967 4002 236969 0559568 2902 3663757 1476669 2902 2415044 11727970 2901 55229 0338671 2902 1731734 7031872 3002 774627 32468

52 Experimental Results and Problems Analysis The resultsof both methods that is the proposed and the referencemethods are examined and compared in all 91 subjects Aunified ldquospanrdquo value described in the reference method [29]which is designed to assess the quality of the methods inremoving the baseline wander is calculated for all cases Thisvalue for all experimental results was 1500 which is the levelidentifying a very high quality of baseline removal

The 91 cases based on the closeness of the results of thetwo methods are divided into two groups The details of theresults are shown for 72 out of 91 subjects in Table 1 for thesesubjects the proposed algorithm achieves almost identicalresults as the reference method The results of the remaining19 subjects which will be discussed separately show thatthe proposed method cannot be able to remove the baselinedrift optimally

In Table 1 ldquoshiftrdquo and ldquoelevationrdquo are the values for adjust-ments to the original independent component (baselinewander) to form the new baseline wander in the horizontaland vertical directions ldquoerror1rdquo represents the differencebetween the old baseline wander (sig

1) before shift and

the baseline wander (sig) from the reference method calcu-lated as follows

error1 =(sig1minus sig)2

119899

(18)

where 119899 is the number of sample points in the baselinewander and finally ldquoerror2rdquo represents the difference between


0100200300400

1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69

Shift

Figure 6 Value of ldquoshiftrdquo that adjusts the old baseline wander toform the new one for all 72 subjects

01234567

1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69

Elevation

Figure 7 Value of ldquoelevationrdquo that adjust the old baseline wander toform the new one for all 72 subjects

the new baseline wander (sig2) and the baseline wander (sig)

from the reference method calculated as follows


119899

(19)

As it can be seen in Table 1 for all cases error2 is significantlysmaller than error1 which shows the impact of thatmethod inldquopurifyingrdquo the baselinewander and creating a better estimateof the drift In order to better assess the performance of theproposed method in removing the baseline wander moreanalyses are conducted on the results

Figures 6 and 7 show the shift and elevation for all 72subjects As can be seen both of these variables are almostthe same for all subjects and do not change across differentsubjects (119909-axis) or vary in a small scope This observationillustrates the reason to adjust the parameters between the oldbaseline wander and the new baseline wander

Figure 8 shows the error reduction in 72 subjects afteradjusting shift and elevation value It can be seen that in allof these cases the errors decrease significantly after adjustingthe baseline wander compared with the baseline wander Theaverage percentage of error reduction Aver119864 reaches up to9013 The formulation of the average percentage of errorreduction is shown in the following

percentage (119894) =(error1 minus error2)

error1 119894 isin [1 119899]

Aver119864 =119894=119899

sum

119894=1

percentage (119894) (20)

where 119894 is the index of subject and 119899 is the total number ofsubjects

Sample signals before baseline removal and after baselineremoval with the proposed method as well as the referencemethod are shown in Figure 9 As shown in Figure 9 theresults of the twomethods in all above-mentioned 72 subjects

0

50

100

1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69

Error improvement ()

Figure 8 Improved percentages of error after adjustment

0 2000 4000 6000 8000 10000minus50

0

50

100

0 2000 4000 6000 8000 10000minus50

0

50

100

0 2000 4000 6000 8000 10000minus50

0

50

100

Original signal

Signal after baseline removal with the proposed method

Signal after baseline removal with the reference method

Figure 9 Comparison between the proposed method and thereference method

are very similar In addition as it can be seen both methodsare very effective in removing the baseline drift

However as mentioned above on the ECG of theremaining 19 subjects the results of the proposed methodand the reference method are not as similar that is thevalue of error2 (which shows the difference between thetwo methods) is significant This is because in these signalsthe inherent pattern observed from ECG is highly distortedhence leading to spurious estimations As mentioned beforewe have visually inspected all 91 cases By examining thesignals for these 19 cases it was discovered that the high valueof error2 does not seem to come from the inability of theproposed method to remove the baseline wander In suchcase the possible reason and improvement are discussed inthe following part

As a comparison between the proposed method andreference method some such sample results are shown inFigure 10 In these cases due to the presence of significantlystronger baseline drifts the reference method seems not tobe eliminating almost all the baseline drift The reason forthis might lie in the fact that the reference method reliesheavily on the parameters set that may work very well forsome ECG signals but not for others As shown in Figure 10our proposed method shows more effective performance inremoving the baseline around times such as 4700 5500 7500and 9500 Another major advantage is that the proposed


0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000minus20

2060

100

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 100000

4080

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000minus202060

100

Original signal



Figure 10 Comparison of the proposed method to the referencemethod

method is computationally faster than the reference methodwhile achieving the same quality of results

53 Further Experimental Analysis of Method As mentionedabove in the experiment multi-channel signals are con-structed through a single-channel signal The multi-channelsignals are constructed using sixty signals which are 10sample point delayed successions of the original signal Byobservation the number of the constructed signals greatlyimpacts the success of finding the true baseline wanderMoreover the degree of delay has a close relationship withthe smoothness of the baseline wander Experimentally it canbe considered thatmore channels and smaller delayed signalsmay achieve better results meaning that the constructedmulti-channel signals may convey enough information inorder to accurately extract the baseline wander

In addition as discussed above the LBNP dataset shows asignificant level of variations in the baseline drift Thereforein further analysis of the method the sub-signals were seg-mented to verify whether the slow changes in the trend of thebaseline wander affect the results of the proposed method inseparating the baseline wander The sub-signals were chosento be only 10000 sample points long from the beginningof the original signal in LBNP dataset Experimental resultsshowed that the slow changing trend of the baseline wanderdid not affect the performance of the proposed method inextracting the baseline wander In other words the baselinedrift with slow changing trends can also be successfullyextracted using the proposed method

6 Conclusion

While using the blind source separation paradigm the ECGbaseline wander or drift may be removed The presentpaper demonstrates a hierarchical method utilizing ICA tosignificantly improve the performance of this process andachieve improved performance Compared with the existingmethods the proposedmethod has the following advantages(1) The proposed method provides more flexibility with

regard to parameter estimation and selection (2) When fol-lowing the steps proposed for adjustment of ICA process thefundamental assumption of baseline noise coming from anindependent source can be further verified which supportsthe validity of using the method for ECG baseline removalSuch an assumption verified by additional experimentalresults would present a chance to remove other types of noise(3) The filtering process proposed for forming the multi-channel signals provides a highly flexible method to form theinput to ICA

References

[1] L T Sheffield A Berson D Bragg-Remschel et al ldquoRecom-mendations for standard of instrumentation and practice in theuse of ambulatory electrocardiographyrdquo Circulation vol 71 no3 pp 626Andash636A 1985

[2] J A van Alste W van Eck and O E Herrmann ldquoECG baselinewander reduction using linear phase filtersrdquo Computers andBiomedical Research vol 19 no 5 pp 417ndash427 1986

[3] L P Harting N M Fedotov and C H Slump ldquoOn baselinedrift suppressing in ECG-recordingsrdquo in Proceedings of the IEEEBenelux Signal Processing Symposium pp 133ndash136 2004

[4] L Sornmo ldquoTime-varying digital filtering of ECG baselinewanderrdquo Medical and Biological Engineering and Computingvol 31 no 5 pp 503ndash508 1993

[5] C R Meyer and H N Keiser ldquoElectrocardiogram baselinenoise estimation and removal using cubic splines and state-space computation techniquesrdquo Computers and BiomedicalResearch vol 10 no 5 pp 459ndash470 1977

[6] C Papaloukas D I Fotiadis A P Liavas A Likas and LK Michalis ldquoA knowledge-based technique for automateddetection of ischaemic episodes in long duration electrocardio-gramsrdquoMedical and Biological Engineering and Computing vol39 no 1 pp 105ndash112 2001

[7] V S Chouhan and S S Mehta ldquoTotal removal of baseline driftfrom ECG signalrdquo in Proceedings of International Conference onComputing Theory and Applications (ICCTA rsquo07) pp 512ndash515March 2007

[8] 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 36 no5 pp 581ndash586 1998

[9] M Blanco-Velasco B Weng and K E Barner ldquoECG signaldenoising and baseline wander correction based on the empir-ical mode decompositionrdquo Computers in Biology and Medicinevol 38 no 1 pp 1ndash13 2008

[10] J Raimon P Laguna N V Thakor and P Caminal ldquoAdaptivebaseline wander removal in the ECG comparative analysiswith cubic spline techniquerdquo in Proceeding of Computers inCardiology pp 143ndash146 October 1992

[11] Z Barati and A Ayatollahi ldquoBaseline wandering removal byusing independent component analysis to single-channel ECGdatardquo in Proceedings of International Conference on Biomedicaland Pharmaceutical Engineering (ICBPE rsquo06) pp 152ndash156December 2006

[12] M P S ChawlaH KVerma andVKumar ldquoArtifacts and noiseremoval in electrocardiograms using independent componentanalysisrdquo International Journal of Cardiology vol 129 no 2 pp278ndash281 2008


[13] M P S Chawla H K Verma and V Kumar ldquoIndependentcomponent analysis a novel technique for removal of artifactsand baseline wander in ECGrdquo in Proceedings of the 3rd NationalControl Instrumentation System Conference pp 14ndash18 2006

[14] M Keralapura M Pourfathi and B Sirkeci-Mergen ldquoImpactof contrast functions in Fast-ICA on twin ECG separationrdquoIAENG International Journal of Computer Science vol 38 no1 pp 38ndash47 2011

[15] K Arfanakis D Cordes V M Haughton C H Moritz MA Quigley and M E Meyerand ldquoCombining independentcomponent analysis and correlation analysis to probe interre-gional connectivity in fMRI task activation datasetsrdquo MagneticResonance Imaging vol 18 no 8 pp 921ndash930 2000

[16] Y Ye Z L Zhang J Zeng and L Peng ldquoA fast and adaptiveICA algorithm with its application to fetal electrocardiogramextractionrdquoAppliedMathematics andComputation vol 205 no2 pp 799ndash806 2008

[17] A Hyvarinen and E Oja ldquoIndependent component analysisalgorithms and applicationsrdquo Neural Networks vol 13 no 4-5pp 411ndash430 2000

[18] M Milanesi N Vanello V Positano et al ldquoFrequency domainapproach to blind source separation in ECG monitoring bywearable systemrdquo in Proceedings of Computers in Cardiology pp767ndash770 September 2005

[19] M Milanesi N Vanello V Positano M F Santarelli and LLandini ldquoSeparation and identification of biomedical signalsbased on frequency domain independent component analysisrdquoWSEAS Transactions on Systems vol 4 no 10 pp 1752ndash17612005

[20] A Hyvarinen ldquoFast and robust fixed-point algorithms forindependent component analysisrdquo IEEE Transactions on NeuralNetworks vol 10 no 3 pp 626ndash634 1999

[21] C J James and O J Gibson ldquoTemporally constrained ICA anapplication to artifact rejection in electromagnetic brain signalanalysisrdquo IEEE Transactions on Biomedical Engineering vol 50no 9 pp 1108ndash1116 2003

[22] J Lee K L Park and K J Lee ldquoTemporally constrained ICA-based foetal ECG separationrdquo Electronics Letters vol 41 no 21pp 1158ndash1160 2005

[23] A Hyvarinen P O Hoyer andM Inki ldquoTopographic indepen-dent component analysisrdquoNeural Computation vol 13 no 7 pp1527ndash1558 2001

[24] V D Calhoun T Adali G D Pearlson and J J Pekar ldquoSpatialand temporal independent component analysis of functionalMRI data containing a pair of task-related waveformsrdquo HumanBrain Mapping vol 13 no 1 pp 43ndash53 2001

[25] B Widrow J R Glover J M McCool et al ldquoAdaptive noisecancelling principles and applicationsrdquo Proceedings of the IEEEvol 63 no 12 pp 1692ndash1716 1975

[26] J R Glover ldquoAdaptive noise canceling applied to sinusoidalinterferencesrdquo IEEE Transactions on Acoustics Speech andSignal Processing vol 25 no 6 pp 484ndash491 1977

[27] A Hyvarinen ldquoNew approximations of differential entropy forindependent component analysis and projection pursuitrdquo inAdvances in Neural Information Processing Systems vol 10 pp273ndash279 1998

[28] S Y Ji A Belle K RWard et al ldquoHeart rate variability analysisduring central hypovolemia using wavelet transformationrdquoJournal of Clinical Monitoring and Computing pp 1ndash14 2013

[29] W S Cleveland ldquoRobust locally weighted regression andsmoothing scatterplotsrdquo Journal of the American StatisticalAssocaition vol 74 pp 829ndash836 1979

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Anatomy Research International

PeptidesInternational Journal of


Hindawi Publishing Corporation httpwwwhindawicom

International Journal of

Volume 2014

Zoology


Molecular Biology International

GenomicsInternational Journal of


The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


BioinformaticsAdvances in

Marine BiologyJournal of



Signal TransductionJournal of


BioMed Research International

Evolutionary BiologyInternational Journal of



Biochemistry Research International

ArchaeaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Genetics Research International


Advances in

Virolog y

Hindawi Publishing Corporationhttpwwwhindawicom

Nucleic AcidsJournal of

Volume 2014

Stem CellsInternational



Enzyme Research



Microbiology


removal distorts and deforms the ECG signal In particu-lar it affects the ST-segment that has very low frequencycomponents Furthermore ectopic beats occurring in theECG during the course of different types of diseases andinjuries change the frequency spectrum of both the baselinewander and the ECG waveforms All the above-mentionedcharacteristics demand a more comprehensive approach thatworks for a wider range of applications and avoids distortingthe main ECG waves when removing the baseline drift

Digital filters are commonly employed method to elimi-nate baseline wander Cut-off frequency and phase responsecharacteristics are two main factors considered in the major-ity of these designsThe use of linear phase filters prevents theissue of phase distortion [2] For finite impulse response (FIR)filters it is rather straightforward to achieve linear phaseresponse directly Feed-forward and feed-back technologiessuch as infinite impulse response (IIR) filters can also provideminimum phase distortion [3] In all of these methods thecut-off frequency should be chosen so that the informationin the ECG signals remains undistorted while the baselinewander is removed which results in a trade-off Usually thecut-off frequency is set according to the slowest detected(or assumed) heart rate However if there are ectopic beatsin the ECG signal it is even more difficult to find thisparticular frequency It is a prevalent phenomenon that theoverlap between the baseline wander and low frequencycomponents of the ECG compromises the accuracy of theextracted features

Time-variant filters are designed to increase flexibility inthe adjustment and control of the cut-off frequency In suchmethods the cut-off frequency of the filter is controlled bythe low frequency characteristics of the ECG signal [4] Cubicspline curve fitting [5] linear spline curve fitting [6] andnonlinear spline curve fitting [7] belong to another family offilters that remove the baselinewander but often require somereference points For instance the linear spline curve fittingmethod [5] forms a subsignal of the ECG for a single cardiaccycle starting 60ms before the P-wave and ending 60ms afterthe T-wave and fits a first order polynomial to this sub-signalafter subtracting the mean of sub-signal Multirate systemwavelet transform has also been utilized for the ECG baselinewander removal The approach using wavelet adaptive filter(WAF) [8] consists of two steps First a wavelet transformdecomposes the ECG signal into seven frequency bands Thesecond step is an adaptive filter that uses the signal of theseventh lowest frequency band as the primary input and aconstant as a reference unit for filtering Another multi-ratesystem empirical mode decomposition (EMD) [9] has alsobeen adopted to eliminate the baseline wander Comparedwith the wavelet technique that uses some predefined basisfunctions to represent a signal EMD relies on a fully data-drivenmechanism that is EMDdoes not require any a-prioriknown basis

Adaptive filters as a cascade structure [10] have also beenused for this application The first step of this approach usesan adaptive notch filter to eliminate the DC component ofthe ECG The second step forms a comb filter assuming thatthe signal is an event-related signal Blind source separation(BSS) in particular independent component analysis (ICA)

[11ndash13] is another choice to remove the baseline wanderAs a specific type of BSS method ICA has been extensivelyused in biomedical signals [14ndash16] such as the ECG and theEEG It has been used as an effective method to decom-pose multichannel signals into fundamental componentsAs many more applications of ICA are being recognizednewer variations of ICA are being introduced Standard ICA[17] (sICA) is a technique that is used to estimate sourcesignals when several mixtures of signals are available Boththe source signals and the mixing process are unknown andthe sources are estimated only on the assumption that theyare statistically independent Comparing the formulation ofthe standard ICA convolutive ICA (fICA) deems that thefinite impulse response is closely associated with the mixingprocess and the mixing process can be considered as aweighted and delayed mixture of sources [18 19] Fast androbust fixed-point ICA [20] is produced based on the ideathat it is feasible to use contrast function to approximatenegentropy Through a fixed-point algorithm the contrastfunction is maximized to extract latent sources with highspeed Temporally constrained ICA [21 22] is a more flexiblemodel to separate latent sources By using prior knowledge oradditional constraints the targeted latent source is extractedMoreover there are many other forms of ICA for differentapplications such as topographic independent componentanalysis [23] and spatial and temporal independent compo-nent analysis [24]

In summary the traditional methods are limited in eitherfrequency delineation or reference choice and the case of BBSin applications mentioned previously does not give sufficientevidence in noise removal Based on these points of view inthe proposed method a unified method utilizing an adaptivenotch filter and BSS is used for baseline drift removal Specif-ically multichannel signals are constructed using a single-channel signal and ICA is applied to the ECG The maincontributions of our work lie in combining the capabilitiesof adaptive filters and BSS expanding the capabilities of theindependent components for this application by customizingthe ICA method towards the removal of the ECG baselinewander Furthermore the factors affecting the performanceof the separation process are explored and improved in thispaper

The rest of the paper is organized as follows The overallstructure of the proposed method is illustrated in Section 2The adaptive notch filter as employed in the paper isdescribed in Section 3 The concepts and formulation of theICA the fast and robust fixed-point ICA and the customizedform are introduced in Section 4 Section 5 introduces theprocess of detecting the components that cause the baselinewander and verifies this process This section also exploresthe factors that affect the separation of the results FinallySection 6 concludes the paper

2 Method

Figure 1 shows the framework of the proposed method As itcan be seen in Figure 1 the first step of the proposed methodis an adaptive notch filter designed to form subsignals ofthe ECG as described later Next as shown in Figure 1


ECG signal



Construct

Old baseline wander

New baseline wander

Residual signal

Filtered ECG signal

Fast ICA

Adjust

Remove

Combine



multichannel signal

















119889119896


1199101119896

119909119909

119910119873119896

119889119896120572

119910119894119896119908119894119896minus1119908119894119896minus1

120576119896



119910119896 = 119908119879

119896119909119896

120576119896 = 119889119896 minus 119910119896

119908119896+1 = 119908119896 + 120597120576119896119909119896

(1)


120573 =

sin (119873119908119903119879)sin (119908119903119879)

(2)


119909 = 119862 cos (119908119903119879 + 120579) (3)


119867(119911) =

119911

2minus 2119911 cos (119908119903119879) + 1

119911

2minus 2 (1 minus 119873120597119862

24) 119911 cos (119908119903119879) + (1 minus 11987312059711986222)

(4)





1199091 (119905) = 119888111199041 + 119888121199042

1199092 (119905) = 119888211199041 + 119888221199042

(5)





119883 = 119862119899times119899 sdot 119878 (7)




119864 (119910) = minussum

119894

119875 (119910 = 119888119894) log119875 (119910 = 119888119894) (8)


119864 (119910) = minusint119891 (119910) log (119891 (119910)) 119889119910 (9)


119869 (119910) = 119864 (119910gauss) minus 119864 (119910) (10)




119869 (119910) =

119901

sum

119894=1

119896119894[119864 (119866119894 (119910)) minus 119864 (119866 (V))]2 (11)


119869 (119910) = [119864 (119866 (119910)) minus 119864 (119866 (V))]2

(12)


1198661 (119910) =

1

1198861

log cosh (1198861119910) 1198921 (119910) = tanh (1198861119910)

1198662 (119910) = minus

1

1198862

exp(minus11988621199102

2

) 1198922 (119910) = 119910 exp(minus11988621199102

2

)

1198663 (119910) =

1

4

119910

4 1198923 (119910) = 119910

3

(13)



119864 119910119910

119879 = 119863119881119863

119879 (14)


119911 = 119863119881

minus12119863

119879119910 (15)


119911 = 119863119881

12119863

119879119862119904 =

119862119904 (16)



criteria 1199081015840 = 119864119909119892(119908

119879119909) minus 119864119892

1015840(119908

119879119909)119908 and nor-


1015840119908

1015840






5 Results






0 002 004 006 008 01minus04

minus02

0

02

04

06

08

1

(a)

0 0002 0004 0006 0008 001 0012minus04

minus02

0

02

04

06

08

1

(b)


0 50 100 150 200 2500

02040608

11214

Mag

nitu

de

Frequency (Hz)

(a)

0 50 100 150 200 2500

02040608

11214

Mag

nitu

de

Frequency (Hz)

(b)


0 50 100 150 200 2500

02

04

06

08

1

12

14

Mag

nitu

de

Frequency (Hz)




BW =

119873120597119862

2

2119879

(rads) (17)






Error2

1 2900 20996 078472 2501 281832 270373 3004 1939524 344954 3001 243905 107275 3003 891358 362826 2902 179017 116147 3001 28955 106238 2000 1077542 1344399 3002 2038138 4084610 2902 817942 2281811 2902 2563747 8726412 3002 410977 2422313 2601 442238 227914 2602 1017592 2331715 3102 7001481 10142916 2901 127575 1352217 2901 456429 2641218 3100 368833 11822419 2901 91224 18820 2902 1813923 23019321 3002 254492 2642122 3704 2524353 8561623 2602 3047066 7463724 2901 1169048 37725 3001 163922 10526 2900 34748 0667127 3002 1444347 1857928 2900 239724 2164129 2901 145089 0220530 2901 1553859 3670731 3001 506959 2675732 3001 272665 110133 3001 567045 199934 2902 3244399 10031335 3001 426266 0879136 2902 5397357 31323837 2901 198874 0813138 2901 143623 2649939 2601 88582 6478740 3004 1350286 3005641 2901 295551 2754142 3001 433923 3005243 2900 510465 6924144 2900 319213 5464645 2901 97597 1332846 2701 227897 1359847 2902 935265 189948 2900 87422 1560749 3506 892829 74303450 3003 2094986 63436

Table 1 Continued





1) before shift and



119899

(18)



0100200300400

1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69

Shift


01234567

1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69

Elevation





119899

(19)





error1 119894 isin [1 119899]

Aver119864 =119894=119899

sum

119894=1




0

50

100

1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69



0 2000 4000 6000 8000 10000minus50

0

50

100

0 2000 4000 6000 8000 10000minus50

0

50

100

0 2000 4000 6000 8000 10000minus50

0

50

100

Original signal








0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000minus20

2060

100

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 100000

4080

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000minus202060

100

Original signal







6 Conclusion



References






































Volume 2014

Zoology






















Advances in

Virolog y



Volume 2014




Enzyme Research



Microbiology


ECG signal



Construct

Old baseline wander

New baseline wander

Residual signal

Filtered ECG signal

Fast ICA

Adjust

Remove

Combine



multichannel signal

















119889119896


1199101119896

119909119909

119910119873119896

119889119896120572

119910119894119896119908119894119896minus1119908119894119896minus1

120576119896



119910119896 = 119908119879

119896119909119896

120576119896 = 119889119896 minus 119910119896

119908119896+1 = 119908119896 + 120597120576119896119909119896

(1)


120573 =

sin (119873119908119903119879)sin (119908119903119879)

(2)


119909 = 119862 cos (119908119903119879 + 120579) (3)


119867(119911) =

119911

2minus 2119911 cos (119908119903119879) + 1

119911

2minus 2 (1 minus 119873120597119862

24) 119911 cos (119908119903119879) + (1 minus 11987312059711986222)

(4)





1199091 (119905) = 119888111199041 + 119888121199042

1199092 (119905) = 119888211199041 + 119888221199042

(5)





119883 = 119862119899times119899 sdot 119878 (7)




119864 (119910) = minussum

119894

119875 (119910 = 119888119894) log119875 (119910 = 119888119894) (8)


119864 (119910) = minusint119891 (119910) log (119891 (119910)) 119889119910 (9)


119869 (119910) = 119864 (119910gauss) minus 119864 (119910) (10)




119869 (119910) =

119901

sum

119894=1

119896119894[119864 (119866119894 (119910)) minus 119864 (119866 (V))]2 (11)


119869 (119910) = [119864 (119866 (119910)) minus 119864 (119866 (V))]2

(12)


1198661 (119910) =

1

1198861

log cosh (1198861119910) 1198921 (119910) = tanh (1198861119910)

1198662 (119910) = minus

1

1198862

exp(minus11988621199102

2

) 1198922 (119910) = 119910 exp(minus11988621199102

2

)

1198663 (119910) =

1

4

119910

4 1198923 (119910) = 119910

3

(13)



119864 119910119910

119879 = 119863119881119863

119879 (14)


119911 = 119863119881

minus12119863

119879119910 (15)


119911 = 119863119881

12119863

119879119862119904 =

119862119904 (16)



criteria 1199081015840 = 119864119909119892(119908

119879119909) minus 119864119892

1015840(119908

119879119909)119908 and nor-


1015840119908

1015840






5 Results






0 002 004 006 008 01minus04

minus02

0

02

04

06

08

1

(a)

0 0002 0004 0006 0008 001 0012minus04

minus02

0

02

04

06

08

1

(b)


0 50 100 150 200 2500

02040608

11214

Mag

nitu

de

Frequency (Hz)

(a)

0 50 100 150 200 2500

02040608

11214

Mag

nitu

de

Frequency (Hz)

(b)


0 50 100 150 200 2500

02

04

06

08

1

12

14

Mag

nitu

de

Frequency (Hz)




BW =

119873120597119862

2

2119879

(rads) (17)






Error2

1 2900 20996 078472 2501 281832 270373 3004 1939524 344954 3001 243905 107275 3003 891358 362826 2902 179017 116147 3001 28955 106238 2000 1077542 1344399 3002 2038138 4084610 2902 817942 2281811 2902 2563747 8726412 3002 410977 2422313 2601 442238 227914 2602 1017592 2331715 3102 7001481 10142916 2901 127575 1352217 2901 456429 2641218 3100 368833 11822419 2901 91224 18820 2902 1813923 23019321 3002 254492 2642122 3704 2524353 8561623 2602 3047066 7463724 2901 1169048 37725 3001 163922 10526 2900 34748 0667127 3002 1444347 1857928 2900 239724 2164129 2901 145089 0220530 2901 1553859 3670731 3001 506959 2675732 3001 272665 110133 3001 567045 199934 2902 3244399 10031335 3001 426266 0879136 2902 5397357 31323837 2901 198874 0813138 2901 143623 2649939 2601 88582 6478740 3004 1350286 3005641 2901 295551 2754142 3001 433923 3005243 2900 510465 6924144 2900 319213 5464645 2901 97597 1332846 2701 227897 1359847 2902 935265 189948 2900 87422 1560749 3506 892829 74303450 3003 2094986 63436

Table 1 Continued





1) before shift and



119899

(18)



0100200300400

1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69

Shift


01234567

1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69

Elevation





119899

(19)





error1 119894 isin [1 119899]

Aver119864 =119894=119899

sum

119894=1




0

50

100

1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69



0 2000 4000 6000 8000 10000minus50

0

50

100

0 2000 4000 6000 8000 10000minus50

0

50

100

0 2000 4000 6000 8000 10000minus50

0

50

100

Original signal








0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000minus20

2060

100

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 100000

4080

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000minus202060

100

Original signal







6 Conclusion



References






































Volume 2014

Zoology






















Advances in

Virolog y



Volume 2014




Enzyme Research



Microbiology







119889119896


1199101119896

119909119909

119910119873119896

119889119896120572

119910119894119896119908119894119896minus1119908119894119896minus1

120576119896



119910119896 = 119908119879

119896119909119896

120576119896 = 119889119896 minus 119910119896

119908119896+1 = 119908119896 + 120597120576119896119909119896

(1)


120573 =

sin (119873119908119903119879)sin (119908119903119879)

(2)


119909 = 119862 cos (119908119903119879 + 120579) (3)


119867(119911) =

119911

2minus 2119911 cos (119908119903119879) + 1

119911

2minus 2 (1 minus 119873120597119862

24) 119911 cos (119908119903119879) + (1 minus 11987312059711986222)

(4)





1199091 (119905) = 119888111199041 + 119888121199042

1199092 (119905) = 119888211199041 + 119888221199042

(5)





119883 = 119862119899times119899 sdot 119878 (7)




119864 (119910) = minussum

119894

119875 (119910 = 119888119894) log119875 (119910 = 119888119894) (8)


119864 (119910) = minusint119891 (119910) log (119891 (119910)) 119889119910 (9)


119869 (119910) = 119864 (119910gauss) minus 119864 (119910) (10)




119869 (119910) =

119901

sum

119894=1

119896119894[119864 (119866119894 (119910)) minus 119864 (119866 (V))]2 (11)


119869 (119910) = [119864 (119866 (119910)) minus 119864 (119866 (V))]2

(12)


1198661 (119910) =

1

1198861

log cosh (1198861119910) 1198921 (119910) = tanh (1198861119910)

1198662 (119910) = minus

1

1198862

exp(minus11988621199102

2

) 1198922 (119910) = 119910 exp(minus11988621199102

2

)

1198663 (119910) =

1

4

119910

4 1198923 (119910) = 119910

3

(13)



119864 119910119910

119879 = 119863119881119863

119879 (14)


119911 = 119863119881

minus12119863

119879119910 (15)


119911 = 119863119881

12119863

119879119862119904 =

119862119904 (16)



criteria 1199081015840 = 119864119909119892(119908

119879119909) minus 119864119892

1015840(119908

119879119909)119908 and nor-


1015840119908

1015840






5 Results






0 002 004 006 008 01minus04

minus02

0

02

04

06

08

1

(a)

0 0002 0004 0006 0008 001 0012minus04

minus02

0

02

04

06

08

1

(b)


0 50 100 150 200 2500

02040608

11214

Mag

nitu

de

Frequency (Hz)

(a)

0 50 100 150 200 2500

02040608

11214

Mag

nitu

de

Frequency (Hz)

(b)


0 50 100 150 200 2500

02

04

06

08

1

12

14

Mag

nitu

de

Frequency (Hz)




BW =

119873120597119862

2

2119879

(rads) (17)






Error2

1 2900 20996 078472 2501 281832 270373 3004 1939524 344954 3001 243905 107275 3003 891358 362826 2902 179017 116147 3001 28955 106238 2000 1077542 1344399 3002 2038138 4084610 2902 817942 2281811 2902 2563747 8726412 3002 410977 2422313 2601 442238 227914 2602 1017592 2331715 3102 7001481 10142916 2901 127575 1352217 2901 456429 2641218 3100 368833 11822419 2901 91224 18820 2902 1813923 23019321 3002 254492 2642122 3704 2524353 8561623 2602 3047066 7463724 2901 1169048 37725 3001 163922 10526 2900 34748 0667127 3002 1444347 1857928 2900 239724 2164129 2901 145089 0220530 2901 1553859 3670731 3001 506959 2675732 3001 272665 110133 3001 567045 199934 2902 3244399 10031335 3001 426266 0879136 2902 5397357 31323837 2901 198874 0813138 2901 143623 2649939 2601 88582 6478740 3004 1350286 3005641 2901 295551 2754142 3001 433923 3005243 2900 510465 6924144 2900 319213 5464645 2901 97597 1332846 2701 227897 1359847 2902 935265 189948 2900 87422 1560749 3506 892829 74303450 3003 2094986 63436

Table 1 Continued





1) before shift and



119899

(18)



0100200300400

1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69

Shift


01234567

1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69

Elevation





119899

(19)





error1 119894 isin [1 119899]

Aver119864 =119894=119899

sum

119894=1




0

50

100

1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69



0 2000 4000 6000 8000 10000minus50

0

50

100

0 2000 4000 6000 8000 10000minus50

0

50

100

0 2000 4000 6000 8000 10000minus50

0

50

100

Original signal








0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000minus20

2060

100

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 100000

4080

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000minus202060

100

Original signal







6 Conclusion



References






































Volume 2014

Zoology






















Advances in

Virolog y



Volume 2014




Enzyme Research



Microbiology




119869 (119910) =

119901

sum

119894=1

119896119894[119864 (119866119894 (119910)) minus 119864 (119866 (V))]2 (11)


119869 (119910) = [119864 (119866 (119910)) minus 119864 (119866 (V))]2

(12)


1198661 (119910) =

1

1198861

log cosh (1198861119910) 1198921 (119910) = tanh (1198861119910)

1198662 (119910) = minus

1

1198862

exp(minus11988621199102

2

) 1198922 (119910) = 119910 exp(minus11988621199102

2

)

1198663 (119910) =

1

4

119910

4 1198923 (119910) = 119910

3

(13)



119864 119910119910

119879 = 119863119881119863

119879 (14)


119911 = 119863119881

minus12119863

119879119910 (15)


119911 = 119863119881

12119863

119879119862119904 =

119862119904 (16)



criteria 1199081015840 = 119864119909119892(119908

119879119909) minus 119864119892

1015840(119908

119879119909)119908 and nor-


1015840119908

1015840






5 Results






0 002 004 006 008 01minus04

minus02

0

02

04

06

08

1

(a)

0 0002 0004 0006 0008 001 0012minus04

minus02

0

02

04

06

08

1

(b)


0 50 100 150 200 2500

02040608

11214

Mag

nitu

de

Frequency (Hz)

(a)

0 50 100 150 200 2500

02040608

11214

Mag

nitu

de

Frequency (Hz)

(b)


0 50 100 150 200 2500

02

04

06

08

1

12

14

Mag

nitu

de

Frequency (Hz)




BW =

119873120597119862

2

2119879

(rads) (17)






Error2

1 2900 20996 078472 2501 281832 270373 3004 1939524 344954 3001 243905 107275 3003 891358 362826 2902 179017 116147 3001 28955 106238 2000 1077542 1344399 3002 2038138 4084610 2902 817942 2281811 2902 2563747 8726412 3002 410977 2422313 2601 442238 227914 2602 1017592 2331715 3102 7001481 10142916 2901 127575 1352217 2901 456429 2641218 3100 368833 11822419 2901 91224 18820 2902 1813923 23019321 3002 254492 2642122 3704 2524353 8561623 2602 3047066 7463724 2901 1169048 37725 3001 163922 10526 2900 34748 0667127 3002 1444347 1857928 2900 239724 2164129 2901 145089 0220530 2901 1553859 3670731 3001 506959 2675732 3001 272665 110133 3001 567045 199934 2902 3244399 10031335 3001 426266 0879136 2902 5397357 31323837 2901 198874 0813138 2901 143623 2649939 2601 88582 6478740 3004 1350286 3005641 2901 295551 2754142 3001 433923 3005243 2900 510465 6924144 2900 319213 5464645 2901 97597 1332846 2701 227897 1359847 2902 935265 189948 2900 87422 1560749 3506 892829 74303450 3003 2094986 63436

Table 1 Continued





1) before shift and



119899

(18)



0100200300400

1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69

Shift


01234567

1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69

Elevation





119899

(19)





error1 119894 isin [1 119899]

Aver119864 =119894=119899

sum

119894=1




0

50

100

1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69



0 2000 4000 6000 8000 10000minus50

0

50

100

0 2000 4000 6000 8000 10000minus50

0

50

100

0 2000 4000 6000 8000 10000minus50

0

50

100

Original signal








0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000minus20

2060

100

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 100000

4080

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000minus202060

100

Original signal







6 Conclusion



References






































Volume 2014

Zoology






















Advances in

Virolog y



Volume 2014




Enzyme Research



Microbiology


0 002 004 006 008 01minus04

minus02

0

02

04

06

08

1

(a)

0 0002 0004 0006 0008 001 0012minus04

minus02

0

02

04

06

08

1

(b)


0 50 100 150 200 2500

02040608

11214

Mag

nitu

de

Frequency (Hz)

(a)

0 50 100 150 200 2500

02040608

11214

Mag

nitu

de

Frequency (Hz)

(b)


0 50 100 150 200 2500

02

04

06

08

1

12

14

Mag

nitu

de

Frequency (Hz)




BW =

119873120597119862

2

2119879

(rads) (17)






Error2

1 2900 20996 078472 2501 281832 270373 3004 1939524 344954 3001 243905 107275 3003 891358 362826 2902 179017 116147 3001 28955 106238 2000 1077542 1344399 3002 2038138 4084610 2902 817942 2281811 2902 2563747 8726412 3002 410977 2422313 2601 442238 227914 2602 1017592 2331715 3102 7001481 10142916 2901 127575 1352217 2901 456429 2641218 3100 368833 11822419 2901 91224 18820 2902 1813923 23019321 3002 254492 2642122 3704 2524353 8561623 2602 3047066 7463724 2901 1169048 37725 3001 163922 10526 2900 34748 0667127 3002 1444347 1857928 2900 239724 2164129 2901 145089 0220530 2901 1553859 3670731 3001 506959 2675732 3001 272665 110133 3001 567045 199934 2902 3244399 10031335 3001 426266 0879136 2902 5397357 31323837 2901 198874 0813138 2901 143623 2649939 2601 88582 6478740 3004 1350286 3005641 2901 295551 2754142 3001 433923 3005243 2900 510465 6924144 2900 319213 5464645 2901 97597 1332846 2701 227897 1359847 2902 935265 189948 2900 87422 1560749 3506 892829 74303450 3003 2094986 63436

Table 1 Continued





1) before shift and



119899

(18)



0100200300400

1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69

Shift


01234567

1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69

Elevation





119899

(19)





error1 119894 isin [1 119899]

Aver119864 =119894=119899

sum

119894=1




0

50

100

1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69



0 2000 4000 6000 8000 10000minus50

0

50

100

0 2000 4000 6000 8000 10000minus50

0

50

100

0 2000 4000 6000 8000 10000minus50

0

50

100

Original signal








0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000minus20

2060

100

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 100000

4080

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000minus202060

100

Original signal







6 Conclusion



References






































Volume 2014

Zoology






















Advances in

Virolog y



Volume 2014




Enzyme Research



Microbiology




Error2

1 2900 20996 078472 2501 281832 270373 3004 1939524 344954 3001 243905 107275 3003 891358 362826 2902 179017 116147 3001 28955 106238 2000 1077542 1344399 3002 2038138 4084610 2902 817942 2281811 2902 2563747 8726412 3002 410977 2422313 2601 442238 227914 2602 1017592 2331715 3102 7001481 10142916 2901 127575 1352217 2901 456429 2641218 3100 368833 11822419 2901 91224 18820 2902 1813923 23019321 3002 254492 2642122 3704 2524353 8561623 2602 3047066 7463724 2901 1169048 37725 3001 163922 10526 2900 34748 0667127 3002 1444347 1857928 2900 239724 2164129 2901 145089 0220530 2901 1553859 3670731 3001 506959 2675732 3001 272665 110133 3001 567045 199934 2902 3244399 10031335 3001 426266 0879136 2902 5397357 31323837 2901 198874 0813138 2901 143623 2649939 2601 88582 6478740 3004 1350286 3005641 2901 295551 2754142 3001 433923 3005243 2900 510465 6924144 2900 319213 5464645 2901 97597 1332846 2701 227897 1359847 2902 935265 189948 2900 87422 1560749 3506 892829 74303450 3003 2094986 63436

Table 1 Continued





1) before shift and



119899

(18)



0100200300400

1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69

Shift


01234567

1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69

Elevation





119899

(19)





error1 119894 isin [1 119899]

Aver119864 =119894=119899

sum

119894=1




0

50

100

1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69



0 2000 4000 6000 8000 10000minus50

0

50

100

0 2000 4000 6000 8000 10000minus50

0

50

100

0 2000 4000 6000 8000 10000minus50

0

50

100

Original signal








0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000minus20

2060

100

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 100000

4080

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000minus202060

100

Original signal







6 Conclusion



References






































Volume 2014

Zoology






















Advances in

Virolog y



Volume 2014




Enzyme Research



Microbiology


0100200300400

1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69

Shift


01234567

1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69

Elevation





119899

(19)





error1 119894 isin [1 119899]

Aver119864 =119894=119899

sum

119894=1




0

50

100

1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69



0 2000 4000 6000 8000 10000minus50

0

50

100

0 2000 4000 6000 8000 10000minus50

0

50

100

0 2000 4000 6000 8000 10000minus50

0

50

100

Original signal








0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000minus20

2060

100

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 100000

4080

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000minus202060

100

Original signal







6 Conclusion



References






































Volume 2014

Zoology






















Advances in

Virolog y



Volume 2014




Enzyme Research



Microbiology


0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000minus20

2060

100

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 100000

4080

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000minus202060

100

Original signal







6 Conclusion



References






































Volume 2014

Zoology






















Advances in

Virolog y



Volume 2014




Enzyme Research



Microbiology


























Volume 2014

Zoology






















Advances in

Virolog y



Volume 2014




Enzyme Research



Microbiology








Volume 2014

Zoology






















Advances in

Virolog y



Volume 2014




Enzyme Research



Microbiology

Documents

Research Article A Hierarchical Method for Removal of ...downloads.hindawi.com/journals/tswj/2013/896056.pdfResearch Article A Hierarchical Method for Removal of Baseline Drift from