REMOVAL OF ELECTRODE MOTION ARTIFACT IN ECG SIGNALS USING WAVELET BASED THRESHOLD METHODS WITH GREY INCIDENCE DEGREE

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1 Removal of Electrode Moton Artfact n Ecg Sgnals Usng Wavelet Based Threshold Methods wth Grey Incdence Degree REMOVAL OF ELECTRODE MOTION ARTIFACT IN ECG SIGNALS USING WAVELET BASED THRESHOLD METHODS WITH GREY INCIDENCE DEGREE G. UMAMAHESWARA REDDY & M. MURALIDHAR, Dept. of Electroncs and Communcaton Engneerng, Sr Venkateswara Unversty College of Engneerng, Sr Venkateswara Unversty, Trupat , Andhra Pradesh, Inda E-mal : umaskt@gmal.com, muraldhar66@gmal.com Abstract - Cardovascular dseases are one of the most frequent and dangerous problems n modern socety n nowadays. Unfortunately electrocardograms (ECG) sgnals, durng ther acquston process, are affected by varous types of nose and artfacts due to the movement, or breathng of the patent, electrode contact, power-lne nterferences, etc. The am of ths study was to develop an algorthm to remove electrode moton artfact n ECG sgnals. Donoho and Johnstone proposed Wavelet thresholdng de-nosng method based on dscrete wavelet transform (DWT) s sutable for non-statonary sgnals. The wavelet transform coeffcent s processed by usng grey relaton analyss of the grey theory, and a new wavelet threshold method namely wavelet threshold method wth grey ncdence degree (GID) (or the GID threshold method) based s ntroduced. It shows that the sgnal smoothness and smlarty of the two sgnal crtera have been greatly mproved by the GID threshold method compared wth exstng threshold methods. Accordng to the characterstcs of dfferent ECG sgnals, GID threshold method gets better results than t can adaptvely deal wth nose separaton and detals remanng of the two opposng sgnal problems, so as to provde a better choce for wavelet threshold methods of sgnal processng. Performance analyss was performed by evaluatng Mean Square Error (MSE), Sgnal-to-nose rato (SNR) and vsual nspecton over the denosed sgnal from each algorthm. The expermental result shows that GID hard shrnkage method wth sub-band or level dependent thresholdng gves the best denosng performance on ECG sgnal. The result shows that soft threshold not always gves better denosng performance; t depends on whch wavelet thresholdng algorthm was chosen. Keywords - ECG sgnal, wavelet - based de-nosng, grey ncdence degree, BayesShrnk threshold, MSE. I. INTRODUCTION Moton artfacts are transent base lne changes caused by changes n the electrode-skn mpedance wth electrode moton. Movement of the electrode away from the contact area on the skn, leadng to varatons n the mpedance between the electrode and skn causng potental varatons n the varatons n the ECG and usually manfestng themselves as rapd but contnuous baselne umps or complete saturaton for up to.5 sec [3]. The artfact caused due to electrode s moton. It s a transent nterference caused by loss of contact between the electrode and the skn that effectvely dsconnects the measurement system from the subect. The loss of contact can be permanent, or can be ntermttent as would be the case when a loose electrode s brought n and out of contact wth the skn as a result of movements and vbraton. The usual cause of moton artfacts wll be assumed to be vbratons or movements of the subects. Ths type of nterference represents an abrupt shft n base lne due to movement of the patent whle the ECG s beng recorded [, ]. It s smulated by addng a dc bas for a gven segment of ECG. Electrode moton artfact s generally consdered the most troublesome, snce t can mmc the appearance of ectopc beats and cannot be removed easly by smple flters, as can nose of other types [4]. The electrode used for provdng electrcal contact between the skn and the lead cable can be modeled as a network of equvalent resstors and capactors representng electrcal parameters of dfferent layers of the skn and the skn electrode nterface. The values of these electrcal parameters may be altered due to relatve moton of the electrodes or skn stretch or contact []. Ths means that the equvalent mpedance of the skn and the skn electrode nterface gets dsturbed due to any such acton whch results an artfact known as electrode moton artfact [3]. Unfortunately the moton artfact has a sgnfcant overlap wth spectrum of the ECG sgnal n the frequency range - Hz and hence t s very dffcult to handle ths type of artfact. It s notced that the moton artfact s more abrupt and dstnct n nature as opposed to the slow baselne wander caused due to reparaton. The moton artfact poses a maor challenge n the long term cardac montorng [, ]. Donoho and Johnstone proposed Wavelet thresholdng de-nosng method based on dscrete wavelet transform (DWT) s sutable for nonstatonary sgnals [6, 7, 8, 9, ]. The wavelet transform coeffcent s processed by usng grey relaton analyss of the grey theory, and a new wavelet threshold method namely wavelet threshold method wth grey ncdence degree (GID) (or the GID threshold method) based s ntroduced [4, 5, 6]. In the process of denosng the sgnal by wavelet, the core of the steps s that the threshold acts on the coeffcent of the wavelet decomposton, because the qualty and effect of denosng are nfluenced Internatonal Journal of Electrcal and Electroncs Engneerng (IJEEE), ISSN (PRINT): Vol- Iss-4,

2 Removal of Electrode Moton Artfact n ECG Sgnals usng Wavelet based Threshold methods wth Grey Incdence Degree mmedately by the selecton of the threshold. So a varety of theoretcal and emprcal models have been put forward by many scholars. In the doman of the wavelet transform, the denosng can be dsposed by cuttng the wavelet coeffcents, reducton range of the wavelet coeffcents, and other non-lnear process. The thresholds to coeffcents of the varous layers are generally n accordance wth the SNR of the orgnal sgnal, so as to flterng the nose. Usng ths method, we can avod blurrng the mutaton of sgnal caused by the general low-pass flter to a certan extent, but whch s smlar to the tradtonal low-pass flter wll also cause a lttle loss of sgnal detals. Therefore, we should consder the ssue whch should compromse the sgnal detals remanng and nose suppresson when the method wll be used. Grey system theory researches on uncertanty system of small sample, poor nformaton that s part of nformaton known, part of nformaton unknown, the system s operaton and evoluton s law are descrbed correctly and montored effectvely manly by creatng, developng, extractng the valuable nformaton from the part of known nformaton [4]. Based on that, a new method whch s wavelet threshold method wth grey ncdence degree (GID) (or the GID threshold method) has been proposed n ths paper. It fxes on thresholds of varous wavelet layers accordng to the nose ntensty and the grey ncdence degree between smlar coeffcents and detal coeffcents, and the threshold can also be based on the practcal nose ntensty to adust the coeffcents of grey ncdence degree n the practcal example. GID threshold method can commendably compromse the problem of sgnal detals reman and nose suppresson, so that the sgnal processed by GID has a better smoothness and smlarty. II. THE GREY INCIDENCE ANALYSIS Introducton to the grey ncdence degree: The regresson analyss, varance analyss, prncpal component analyss etc., are the methods for system analyss n the mathematcal statstcs. These methods have ther own defcency, for nstance, they requre large amounts of data, and they would be dffcult to fnd statstcal laws because of less datum and the computng capacty s large, and also they possbly appear as a result that quanttatve analyss doesn t match wth qualtatve analyss, and so on. The basc dea of grey ncdence analyss s based on udgng the extent of ther relaton from the smlarty to sequences of geometrc curve shapes. The closer those are, the greater ncdence degree of the correspondng sequences s and vce versa. Based on ths, we can calculate the grey ncdence degree of the wavelet coeffcents accordng to the smlarty between the approxmate tme sequences (formed by approxmate coeffcents) and the detaled tme sequences (formed by detaled coeffcents). Defnton : Let X be the system factor, f k s the tme seral number, and x (k) s observatonal data for X n the k moment, then X x, x,..., x n s known as the behavoral tme sequence. Defnton : Let X x, x,..., x n be the behavoral tme sequence, and D be the sequence operator, and X D x d, x d,..., x n d where /, x k d x k x x and k =,,, n, then D s called the ntal value operator, and X D s a mappng of X under the D. Theorem : Let the approxmate tme sequence X x, x,..., x n be the system character sequence and let the detaled tme sequence X x, x,..., x n, then the grey ncdence degree between X and X s () n X, X x k, x k x k, x k () n k maxmax mnmn x k x k x k x k k k x k x k x k x k maxmax k Where s known as the dstngushed coeffcent,,, usually, =.5 and the value can be determned by the nose ntensty of the varous layers. The greater s, the greater correspondng s and vce versa. Calculaton of the grey ncdence degree: Accordng to the formula defned by the theorem, we can fnd the steps for calculaton of the grey ncdence degree as follows:. Calculate the mappngs of the ntal values for varous sequences. Let X ' X / x x ', x ',..., x ' n.. where =,,,, N. Calculate the dfference of the mappngs.,,..., n, where Let k x ' k x ' k and =,,,, N. Calculate the bggest dfference and smallest k. Let dfference for k k M m ax m ax and k m m n m n. k Internatonal Journal of Electrcal and Electroncs Engneerng (IJEEE), ISSN (PRINT): Vol- Iss-4,

3 Removal of Electrode Moton Artfact n ECG Sgnals usng Wavelet based Threshold methods wth Grey Incdence Degree v. Calculate the ncdence coeffcents m M k, where, ; k M k =,,, n and =,,,, N. v. Calculate the grey ncdence degree. So n k where =,,,,N. n k mnmn x kx k maxmax x k x k k k k x k, x k x k x k maxmax x kx k (3) III. THE PROCESS OF WAVELET DENOISING Suppose the MIT-BIH ECG data, f n s an orgnal sgnal from k s n polluted by nose, Where e n s the nose and t s supposed as Gaussan whte nose, and s the nose ntensty. The basc nose model can be descrbed as s n f n e n n N,,,...,. (4) The general process of sgnal processed by the wavelet s as follows:. The process of wavelet decomposton: Usng the dscrete wavelet transform by selectng mother wavelet, the nosy sgnal s n s decomposed by the wavelet, at the decomposton level of 5. As a result approxmate coeffcents a and detal coeffcents d were obtaned. Here denotes the level of scalng.. The process of threshold: select an approprate threshold to the coeffcents of varous layers, to obtan the estmated wavelet coeffcents. For each level a threshold value s found, and process detaled coeffcents d through the threshold. 3. Manpulaton of the emprcal wavelet coeffcents: (a) Hard-thresholdng method: d, d d, d (5) Where s the threshold value. 4. The process of sgnal reconstructon: reconstruct the de-nosed ECG sgnal s n d through the wavelet coeffcents processed by threshold, from d and a by usng nverse dscrete wavelet transform (IDWT). From the wavelet denosng process, we can see that the core part of the process s the process of threshold, that s, how to select the threshold of varous layers wll drectly nfluence on the effect of sgnal denosng. The same steps are to be followed for soft thresholdng, de-nosng methods. (b) Soft-thresholdng method: sgn( d )( d ), d d (6), d Threshold selecton: Unversal threshold. ln L, where L s the length of the sgnal, The can be estmated by the wavelet coeffcents wth medan d /.6745 medan ( d. Here ) denotes the medan value of the absolute values of wavelet coeffcents d. Sub-band or level-dependent threshold log d. BayesShrnk threshold: The goal of BayesShrnk method s to mnmze the Bayesan rsk. Thresholdng s done at each band of resoluton n the wavelet decomposton. The Bayes threshold,, s defned as B, where s the nose f varance and s the sgnal varance wthout nose. f Snce the nose and the sgnal are ndependent of each other, t can be stated that can be computed usng the equaton. s s s n s ( n ) (7) n m ax(, ) (8) s f From ths the varance of the sgnal, then Bayes threshold can be computed. B The GID threshold method: The general threshold method s the threshold proposed by Donoho and Johnstone whch they appled the normal, multdmensonal and ndependent decson-makng theory n the Gaussan whte nose model. It s often excessvely smooth true sgnal because the excessve focus on the smoothness of flterng, so that the results show the greater devaton. Based on that, the general threshold s amended by the grey ncdence degree, and then a new threshold value method GID threshold method s proposed, the method not only can flter most of nose, but also t can retan commendably sgnal detals. The threshold of varous layers can be determned, accordng to the grey ncdence degree between wavelet decomposton factor approxmate tme sequences (low frequency) and detaled tme sequences (hgh frequency) and the nose ntensty f f B Internatonal Journal of Electrcal and Electroncs Engneerng (IJEEE), ISSN (PRINT): Vol- Iss-4, 3

4 Removal of Electrode Moton Artfact n ECG Sgnals usng Wavelet based Threshold methods wth Grey Incdence Degree of the levels of the threshold, GID threshold s., where s the grey ncdence GID degree between coeffcents. The concrete steps of the GID flterng nose are as follows:. The wavelet coeffcents wll be ganed by wavelet transform for the sgnal.. Calculate the nose ntensty for varous layers. 3. Calculate the grey ncdence degree between the detaled coeffcents d and approxmate coeffcents a accordng to the equaton (3). 4. Accordng to the wavelet threshold method wth grey ncdence degree (GID), calculate the threshold GID, then keep down the orgnal value when a poston wavelet transform coeffcent value s greater than the threshold, otherwse let the value be zero. IV. DISCUSSION AND CONCLUSION The orthogonal wavelets db4, db5, db6, db8 and sym8 were selected, and the sgnal s(n) s to be decomposed for fve-layer by usng t. Then we threshold the decomposton coeffcents respectvely by Donoho unversal threshold method, Sub-band threshold method, as well as the GID threshold method proposed n ths paper. The orgnal sgnal f (n) s ECG sgnals taken from MIT-BIH arrhythma database [7], and then the moton artfact sgnal from MIT-BIH Nose Stress Test Database [3, 8] of dfferent ntenstes are added to the sgnal. The recordngs were dgtzed at 36 samples per second per channel wth -bt resoluton over a mv range, Fnally, the qualty of the processed sgnal wll be evaluated wth three performance ndexes of the sgnal-to-nose (SNR), mean square error (MSE) and vsual nspecton respectvely. The ECG sgnal 3 wth moton artfact at SNR = -3db s denosed by hard and soft thresoldng methods wth above thresholds mentoned s shown n Fgure. In Fgure. and Fgure 3. Plots for comparson of hard and soft thresholdng methods for thresholds wth and wthout GID on sgnal 3 usng db5 wavelet were shown. By contrast, the GID threshold method proposed n ths paper can not only effectvely suppress nose, but also t commendably retans sgnal detal, so that the denosed sgnal wll mantan well smoothness and smlarty, and that the SNR has been greatly mproved. It flters sgnal by threshold determned by the grey ncdence degree between hgh-frequency coeffcents and low-frequency coeffcents, and by the nose ntensty, whch are combned the wavelet theory wth the grey ncdence analyss, and make use of the nformaton regardng nose and orgnal sgnal n the paper. The experment results show that the GID can commendably solve the compromse problem between the nose suppresson and sgnal detal retanng, t not only loses very few of energy components of the orgnal sgnal, but also the SNR has been greatly mproved. REFERENCES []. G. M. Fresen, T. C. Jannett, M. A. Jadallah, S. L. Yates, S. R. Qunt, H. T. Nagle, A comparson of the nose senstvty of nne QRS detecton algorthms, IEEE Transactons on Bomedcal Engneerng, vol. 3, no., pp , 99. []. V. Shusterman, S. I. Shah, A. Begel, K. P. Anderson Enhancng the precson of ECG baselne correcton: Selectve flterng and removal of resdual error, Computers and Bomedcal Research,, vol. 33, no., pp. 44 6,. [3]. Gar D. Clfford, Francsco Azuae and Patrck McSharry, Advanced Methods and Tools for ECG Data Analyss, Artech House, London, 6. [4]. Amercan Heart Assocatons on Electrocardography, Recommendatons for standardzaton of lead and specfcatons for nstruments n ECG/VCG, Crculaton, 5, pp. -5, 975. [5]. Grzal, F., G. Frangaks, Nose estmaton n ECG sgnals. Proceedngs of the Annual Internatonal conference of the IEEE, 4-7(): 5-53, 988. [6]. F.N. Ucar, M. Korurek, and E. Yazgan, A nose reducton algorthm n ECG sgnals usng wavelet transforms, Bomedcal Engneerng Days, Proceedngs of the 998 nd Internatonal Conference, pp.36-38, 998. [7]. D.L. Donoho and I.M. Johnstone, Ideal spatal adaptaton va wavelet shrnkage, Bometrka, 994, Vol.8, pp [8]. D.L. Donoho, De-nosng by soft thresholdng, IEEE Transactons on Informaton Theory, vol. 4, pp , 995. [9]. D.L. Donoho, and I.M. Johnstone, Adaptng to unknown smoothness va wavelet shrnkage, J. ASA, vol. 9, pp. 3, 995. []. McAdams ET, Jossnet J, Nonlnear transent response of electrode-electrolyte nterface, Medcal and Bologcal Engneerng and Computng, Volume 38, Number 4 (, July), pp , DOI:.7/BF345 []. P.M. Agante and J.P. Marques de S a, ECG nose flterng usng wavelets wth soft-thresholdng methods, Computers n Cardology, vol. 6, pp , 999. []. Odman, S., and Oberg, P., Movement Induced Potentals n Surface Electrodes, Medcal Engneerng and Computng, : 59-66, 98. [3]. Moody GB, Muldrow WE, Mark RG. A nose stress test for arrhythma detectors. Computers n Cardology, :38-384, 984. [4]. Wen-chang We, Jan-l Ca, and Jun-e Yang, A New Wavelet Threshold Method Based on the Grey Incdence Degree and Its Applcaton, Proc. of the Frst Internatonal Conference on Intellgent Networks and Intellgent Systems (ICINIS '8), IEEE Computer Socety Washngton, DC, USA, pp , Nov., 8, do:.9/icinis [5]. Sfeng Lu, Zhgeng Fang and Y Ln, A New Defnton for the Degree of Grey Incdence, Scentfc Inqury: A Journal of Internatonal Insttute for General Systems Studes, Inc. vol. 7, No.,, pp. 4, December, 6. [6]. Sfeng Lu and Y Ln, Grey Informaton Theory and Practcal Applcatons, Sprnger-Verlag London Lmted 6. [7]. nstdb/ [8]. mtdb/. Internatonal Journal of Electrcal and Electroncs Engneerng (IJEEE), ISSN (PRINT): Vol- Iss-4, 4

5 Removal of Electrode Moton Artfact n Ecg Sgnals Usng Wavelet Based Threshold Methods wth Grey Incdence Degree 6 orgnal sgnal nosy sgnal hard unversal thresholdng gd hard unversal thresholdng hard subband thresholdng gd hard subband thresholdng Internatonal Conference on Electrcal and Electroncs Engneerng, ISBN: , 9 th June, -Trupat 5

6 Removal of Electrode Moton Artfact n ECG Sgnals usng Wavelet based Threshold methods wth Grey Incdence Degree 4 hard bayes thresholdng gd hard bayes thresholdng soft unversal thresholdng gd soft unversal thresholdng soft subband thresholdng gd soft subband thresholdng Internatonal Journal of Electrcal and Electroncs Engneerng (IJEEE), ISSN (PRINT): Vol- Iss-4, 6

7 Removal of Electrode Moton Artfact n ECG Sgnals usng Wavelet based Threshold methods wth Grey Incdence Degree 4 soft bayes thresholdng gd soft bayes thresholdng Fg.: Sgnal 3 denosed sgnals from dfferent thresholdng methods for corrupted by em nose of nput SNR = -3 db usng db5 wavelet. Output SNR Input SNR Hard Unversal GID Hard Unversal Hard Subband GID Hard Subband Hard Bayes GID Hard Bayes Output MEAN SQUARE ERROR(MSE) Input SNR Hard Unversal GID Hard Unversal Hard Subband GID Hard Subband Hard Bayes GID Hard Bayes Internatonal Journal of Electrcal and Electroncs Engneerng (IJEEE), ISSN (PRINT): Vol- Iss-4, 7

8 Removal of Electrode Moton Artfact n ECG Sgnals usng Wavelet based Threshold methods wth Grey Incdence Degree (a) (b) Fg. : Plots for comparson of hard thresholdng methods on sgnal 3 usng (a) SNR, (b)mse usng db5 wavelet Output SNR Soft Unversal GID Soft Unversal Soft Subband GID Soft Subband Soft Bayes GID Soft Bayes Output SNR 4 3 Soft Unversal GID Soft Unversal Soft Subband GID Soft Subband Soft Bayes GID Soft Bayes Input SNR Input SNR (a) Fg. 3 : Plots for comparson of soft thresholdng methods on sgnal 3 usng (a)snr, (b) MSE usng db5 wavelet (b). Internatonal Journal of Electrcal and Electroncs Engneerng (IJEEE), ISSN (PRINT): Vol- Iss-4, 8