Đánh giá các thuật toán ICA để loại bỏ các yếu tố nhân tạo từ một kênh đơn ECG

Journal ofScience & Technology 101 (2014) 107-110 Evaluation of ICA Algorithms for Removing Artefacts from A Single-Channel ECG Vuong Hoang Nam'*, Tran Hoai Linh', Nguyen Hoai Giang^ 'Hanoi University of Science and Technology, No.l Dai Co Viet Str, Ha Noi, Viet Nam ^Hanoi Open Univesity Received- February 26, 2014; accepted: Aprd 22 2014 Abstract In this paper, application of Independent Component Analysis (ICA) in removing artefacts from the electrocardiagram (ECG) has been presented In the proposed model, we use ICA for removing noise and artefacts in a single-chanel ECG signal The mam idea of this method is that we use the delay reconstruction to transform the observed univanate ECG signal into a multidimensional matrix.This suggests that artefacts and noise are independent sources from the physiological sources generating the cardiac signals By this way the ICA model can be applied Our goal was to quantify which ICA algorithm would be the most effective More specifically, we were interested in companng the pertormance of FastICA, SOBI and JADE algorithms Computer simulation expenments are presented to illustrate the proposed approach Keywords: ECG, Blind source separation, ICA troduction The electrocardiagram (ECG) signal is a graphical representation of cardiac activity and it used to provide important clinical information, A typical ECG may be corrupted by one or more of the following (1) movement and muscle noise; (2) electncal mterference; (3) A/D conversion; (4) base line dnft In order to employ the ECG signal for medical diagnosis, we have to eliminate the distortions from the ECG Many techniques are based on the spectral decomposition (filtering) of the ECG for removing noise localized in different regions of the frequency spectrum [9] However, these techniques are limited in cases where both noise and signal localized m same regions of the spectrum In this paper, we have presented a Imear BImd Source Separation (BSS) algonthm for removing noise from the ECG BSS is a problem which estimates original source signals using only sensor observations If source signals are mutually independent and non-Gaussian, we can apply the technique of Independent Component Analysis (ICA) to solve a BSS problem [1] Let us formulate the Imear BSS model Suppose that N onginal sources are blindly nuxed and observed Conesponding Author- +84 912,634.666 Email; nam,vuonghoang@mail.bust edu at N sensors Denoting by s n —W 'It , .,s^(ji) the vector of original sources and by X n =\x^ '^ , ,3^;j('i) the observations at sensor, we have linear BSS model: X n =A.s n (1) where A is the unkown mixing matrix In the BSS problem, we try to estimate origmal source signals s n using only sensor observations X n We have to find a hnear transform given by a demixing matrix W , so that y n — W x n with the random variables /^ JI ,I = l,2, ,7Vare as independent and non-Gaussian as possible The applicaUon of BSS/ICA for removing noise from the ECG were presented in some typical works [2,3] and the authours (He T, et al [2] and G.Agrawal et al [3]) used mulhchaimel-ECG recordings to emilmate noise This suggests that artefacts and noise are independent sources fiom the physiological sources generating the cardiac signals In [4] (in Vietnamese), we use FastICA to remove noise and artefacts in a single-chanel ECG recording In this paper, a different study on this method has been made Our goal was to quantify which ICA algorithm would be the most effective More specifically, we were interested in companng the performance of FastICA, SOBI and Journal ofScience & Technology 101 (2014) 107-110 JADE algonthms Computer simulation expenments are presented to illustrate the proposed approach The paper is organized as follows After introduction m Section I, Section II presents Independent Component Analysis, Section III presents the proposed approach Section IV shows the experimental results and some valuable discussions, and the last section is the conclusions, Independent component analysis 2.1 Definition of ICA: ICA of a random vector x consists of finding a linear transformation, y = W x, so that ihe components, J I — l^N , are as independent as possible, in the sense F y^ of maximizing some object fiinction y,^, that measures independence To make the ICA model can be estimated, we have to make certaui assumptions [1]: The original sources s n are assumed statistically independent The onginal sources must have nonGaussian distributions For simplicity, we assume that the unknown mixing matrix A is square, 2.2 Ambiguities of ICA We caimot determine the variances (energies) of the independent component We cannot determine the order of the independent components 2.3 ICA algorithms In order to calculate the de-mixing matrix W , numerous ICA algorithms have been developed with various approaches We have used three of them (FastICA [5,6], SOBI [7] JADE [8]) in our coraparision The proposed approach We denote by A^^ the single-channel ECG signal Let r^ he the sampling time of the ECG so that the signal time senes is x_^ =x(nTj In the linear ICA model, ICA requires as numbers of sensors {ECG leads) as many as numbers of sources Usmg the time delay reconstruction [9], the observed single-channel ECG signal, x^^ = x(nr ) , is transformed into an MxNmatnx: where each column of X contains one time delay reconstructed vector with reconstruction dimension M and delay d The reconstruction dimension M and the time delay d are parameters used to optimize the performance of noise reduction The ICA model may be expressed as X =A S (3) where S an MxA^ matrix containing the mdependent sources (components), A is the M x M m i x i n g mafrix, A" is an Af xiVcontaining the mixed signals The ICA algorithms all performed complete decomposition in which the number of returned components is equal to the number sources ICA algorithms attempt to find a de-mixing mattix W such that S , the ICA estimate of S , is obtained from S = WX (4) ICA learns the de-mixing matnx that makes the component time courses as temporal independeat from each other as possible However, the approach of each ICA algorithm to estimating and/or approaching this independence is different, SOBI [7] is a second-order method that takes advantage of temporal conelations in the source activities Other algorithms, such as so-called FastICA [5,6], maximize the negentropy of their component distributions or their fourth order cummulant(JADE)[8], According to their morphology in the time domain, the ICA components of ECG recording, S, can be divided into three categories, ECG signal, abrupt change and contmuos noise [2] (Fig 1), Statiscal properties of independent components (like kurtosis and variances) were explored to identify the continouos noise and abrapt change [2] Journal ofScience & Technology 101 (2014) 107-110 , *ll|v-i/lfv,Trtfw,,|\^_fl\,-VlV^^ fiiiiii^^^ "V^V^yV;^! (nt nnntlniini: HOISB ' Fig Typical waveforms of (a) - the ECG signal, (b) - abrupt changes, (c) - continuous noise To evaluate the performance of noise reduction, we use a measure of Ihe linear conelation between the cleaned ECG signal z^ and the original noise-free s^, , The cross-conelaUon coefficient/) is given by [9]: where (.) Fig The ECG signal generated by ECGSYN i'l „ 1-^.,^^^- tUL.| denotes the average calculated by summing over the observed time senes indexed by •ii, p and a are the mean and standard deviation of s , II and (7 are the mean and standard deviation of z A value of p ^1 p^—1 reflects a strong conelation, implies a strong an U correlation, and /) as indicates that z_^ and s^ are uncorrelated This mean that a value of /) = suggests that the noise reduction technique has removed all the noise from the observed ECG signal Results and discussion To evaluate the efficiency of the proposed algorithm, experiments are conducted based on syntfietic ECG signals produced by ECGSYN [10] The clean single-channel ECG signals are contaminated by additive white Gaussian noise (AWGN) with the Signal to Noise Ratios (SNRs) of dB and dB In our initial experunent, the SNR= 5dB Fig shows the ECG signal in this experiment generated by ECGSYN with SNR=5dB, Fig The cleaned ECG signal (above) and the separated noise (below) In this experiment, we set a fixed value for the hme delay d = l The conelation is considered as a function of the reconstruction dimension M In the simulation, due to AWGN is a continouos noise so kurtosis value is used to identify It For contmouos noise, kurtosis value is much smaller compared with that of normal ECG [2] Kurtosis can be estimated by using the fourth moment of sample data as follow Kurt x : i\E x' (6) The kurtosis is zero for Gaussian densities In this approach, the cleaned ECG is the component whose modulus of kurtosis is maximum value In the constrary, the separated noise is the component whose modulus of kurtosis is minimum value Fig shows the noise reduction optima (using FastICA) with p = 0,9972 at M = 7, The cleaned ECG, the separated noise are the components with kurt = 7275 and kurt = 0.01347, respectively Journal ofScience & Technolc^ 101 (2014) 107-110 particularly when only one channel of ECG is corrupted Expenments based on AWGN with low SNRs have demonstrated the availability and efficiency of the proposed method Acknowledgement Authors acknowledge the funding pro-vided by Viemam's Ministry of Education and Training, Projectnumber B20I2-01-25 and B20I3-01-42 Fig Vanation in correlation p with econstruction dimension M when d = [1] Aapo Hyvarmen, Juha Karhunen, Erkkl Oja, Independent Component Analysis, John Wiley & Sons Inc., 2001 [2] He Taigang et al "Application of mdependent component analysis in removing artefacts from the ECG", Neural Comput & Appl., 2006, p 105-116 [3] G.Agrawal et al; "Reduction of artifacts in 12channe! ECG signals using FastICA algorilhin", Joumal of ScienUlic & Industnal Research, vol 67, 2008, p 43-48 [4] Virong Hoang Nam, Tran Hoai Linh, Nguyin Qu6c Trung Loai bo nhieu tin hi^u di?n lira ECG bang phircmg phap Phan tich thinh phSn doc l?p, TuySn tap Hoi nghi ty: d^ng h6a VCCA2011, trang 8I3-817,lhang 11/2011 [5] Aapo Hyvarmen, Erkkl Oja : Independent component analysis: Algonthms and Analysis, Neural Networks, 13(2000)411-430 [6] A Hyvarien- Fast and robustfixed-pointalgorithms for independent component analysis, IEEE Trans, on Neural Networks, 10(1999)626-634 [7] A.Belouchrani, K Abed-lvleraim, J,F Cardoso and E.Moulines: A blind source separation technique using second order statistics, IEEE Trans On Sipal Processing, 45 434-444, 1997 [8] Cardoso J F: Higher-order contrasts for independent component analysis Neural ComputaUon, 11 (1999) 157-192 [9] Gari D Clifford et al: Advanced Methods and Tools for ECG Data Analysis, Artech House, 2006 Table Companson of average correlation coeffi between ICA algorithms(SNR=2.5dB) Algorithm JADE P 970 FastICA SOBI 962 0,952 Fig, shows vanation m conelation p with reconstruction dimension, M , when the delay, (f = We used the three ICA algorithms for this simulation In die last experunent, the SNR=2.5 dB In order to make a fair companon of algorithms, we randomly chose ECG signals in the MIT-BIH database All parameters are taken into account In Table I we showed averaged results for the conelation coefficient p The obtained results in Fig.4 and Table I show that the time based on maximizing non-Gaussianity (JADE, FastICA) slightly outperformed the time structure based algonthm (SOBI) We may also conclude that JADE shoud be used for removing artifacts from single-channel ECG signals, as the one with the best quality Conclusions In this paper, application of Independent Component Analysis (ICA) in removing noise and artefacts from a single-channel ECG signal has been presented The main idea of this method is that we use the delay reconstruction to transform the observed univanate ECG signal into a multidimensional manix By this way the ICA model can be applied, ICA can effectively remove a considerable amount of the artefacts and noise [10] http://physionet.org/physiotools/eogsyn/ ... the single-channel ECG signal Let r^ he the sampling time of the ECG so that the signal time senes is x_^ =x(nTj In the linear ICA model, ICA requires as numbers of sensors {ECG leads) as many... FastICA [5,6], maximize the negentropy of their component distributions or their fourth order cummulant(JADE)[8], According to their morphology in the time domain, the ICA components of ECG recording,... conelation between the cleaned ECG signal z^ and the original noise-free s^, , The cross-conelaUon coefficient/) is given by [9]: where (.) Fig The ECG signal generated by ECGSYN i''l „ 1-^.,^^^- tUL.|