A Fast Fractal Model Based ECG Compression Technique Lin Yin 1,a, Fang Yu* 1,b

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1 4th Iteratioal Coferece o Computer, Mechatroics, Cotrol ad Electroic Egieerig (ICCMCEE 2015) A Fast Fractal Model Based ECG Compressio Techique Li Yi 1,a, Fag Yu* 1,b 1 Electroicsad iformatio egieerig college, Togji Uiversity, ShagHai, Chia a fidigsea@163.com, b fagyu@togji.edu.c Keywords: Fractal; Dyamic Compariso Sequece Abstract. ECG moitorig equipmetwill geerate a huge mout of ECG sigals, which causes eormous pressure o server storage ad trasmissio. Therefore, may compressio techiques are proposed to overcome this problem icludig some fractal based lossy ECG compressio techiques. However, basic fractal based techiques caot be used widely o some large-scale applicatios because of its high computatio complexity.i this paper, a improved faster fractal model is proposed to solve this problem. The most importat ad time-cost step i the basic fractal model is the compariso of rage ad domai blocks. Traditioally, the compariso sequece is fixed ad static. I the ew improved fractal model, the sequece is chaged to be dyamic toaccelerate the compressio. It is foud that the improved fractal based techique ca achieve same compressio ratio ad similar Percetage Residual Differece(PRD) error with 4 times faster tha the basic fractal basedtechique. Itroductio The amout of ECG sigal geerated by kids ofmoitor equipmetis huge, so it brigs tremedous pressure o data storage to hospital ad data storage service providers. Meawhile, may e-health applicatios ad healthcare orgaizatios require access to these records, soit brigs pressure o trasmissio. Especially, mobile healthcare is icreasig to a great extet aroud global i recetly years ad itexacerbates these two problems udoubtedly. I order to reduce the pressure o storage ad trasmissio, may ECG compressio techiques have bee created ad implemeted. Geerally, these techiques ca be divided ito two mai categories: lossless ad lossy compressio. Losslesstechiques ca keep the full structure of origi ECG sigal without losig ay iformatio, but its compressio ratio is low ad caot satisfy the requiremet of large applicatios. O the other had, although lossy techique just recostruct approximated versio of the origi ECG sigal, the differeces betwee the origi ECG sigal ad the recostructed ECG sigal are very small, so hospitals ad healthcare sectors still ca use the recostructed sigal o medical research ad diagosis. More importatly, with lossy compressio techique, it is possible to achieve higher compressio ratio. There are two major types i lossy compressio: time domai compressio techiques [1-3] ad trasform domai techiques [4-7]. Wavelet-based techique [4], real-time ECG compressio ad trasmissio techique [5], 1D to 2D compressio techique [6] ad a ECG compressio usig Jpeg2000 algorithm [7]are all wellkow ad excellet ECG compressio techiques. But i the term of compressio ratio, they ca tcompare with fractal based techique.thesetechiques metioed above ca achieve 10 to 30 compressio ratio while fractal based techique ca achieve more tha 40 compressio ratio [8-9].Most of existig compressio techiques o matter time domai or trasform domaiare based o R peak detectio or other ECG parameter detectio [9]. Therefore, they ca ot provide high compressio ratio performace like fractal based techiques sice the fractal model has a huge advatage i dealig with such sigal with self-similarity characteristic.it has bee proved that the periodic self-similarity characteristic of the ECG sigal ca be a powerful feature to be used i fractal based compressio techiques [9]. The proposed techique i this paper is based o fractal model. At preset, the biggest problem i fractal based techiquesis effectiveess. Although usig fractal model ca achieve higher compressio ratio, the process of compressio is so complicated The authors - Published by Atlatis Press 150

2 that whole algorithm requires a lot of time to execute. It is the mai reaso that fractal based techique have t bee used i idustry-level applicatios widely ow. The major goal of this papers is to reduce the executio time of the basic fractal based techique.the most time-cost part of fractal based techiqueis the compariso of rage ad domai blocks. I the compariso process of fractal model, each rage block eeds to compare with each domai block to fid the most similaroe. Fially, the idexes of the most similar domai block ad some related parameters are stored ito the compressed file. I order to improve the fractal based techique, dyamic compariso sequece is proposed i this paper to reduce the umber of compariso of rage ad domai blocks. Dyamic compariso sequecemakes each rage block to fid the domai that meets the requiremet without comparig whole domai blocks.the fractal model usig dyamic domai sequece is implemeted i this paper ad evaluatedby three importat measures: compressio ratio, sigal recostructio error ad compressio executio time. Experimet results shows that the proposed improved fractal based techique ca achieve same compressio ratio ad similar recostructio error with oly ¼ compressio time of the basic fractal based techique. Related work May researchers have coducted ivestigatio o fractal based ECG compressiotechiques. A. Khalaj ad H. Miar Naimi proposed ew efficiet fractal based compressio method for electrocardiogram sigals[8]. Their method is based o the fractal model ad IFS(Iterated Fuctio System). I their model the origi ECG sigal is divided ito o-overlapped blocks called rage ad the dow-sampled copy versio is divided ito overlapped blocks called domai. For each rage block, their method fid the most similar domai the geerates the fractal trasformatio parameters. The fial compressed file store the idexes of rage ad domai blocks ad the parameters. The idexes ad parameters are used to recostructio the ECG sigal. Ayma Ibaida, Dhiah Al-Shammary ad Ibrahim Khalil proposed a cloud eable fractal based ECG compressio techique[9]. Their work is somewhat similar to A. Khalaj ad H. Miar Naimi s, i their method they used two trasformatio parameters whe i A. Khalaj ad H. Miar Naimi s oly oe parameter is used. Their techique ca achieve high compressio ratio with low recostructio error. Accordig to Ayma Ibaida s paper [9], The self-similarity characteristic of ECG sigal is powerful feature that ca be used i fractal model.the improved fractal model proposed i this paper is based o their model ad ca achieve same compressio ratio ad similar recostructio error with less compressio time. The evaluatio sectio shows the compressio performace compariso. The basic coefficiets used to describe the trasformatio relatioship are scale (S) ad offset (O).The scale coefficiet is defied as the greatest differece amog ECG istaces i the rage block divided by the greatest differece amog the ECG istaces i the domai block. Eq. (1) shows the calculatio of scale coefficiet[10]. i=1 D(i)R(i) i=1 R(i) i=1 D(i) S = (1) i=1 i=1 ) 2 D(i) 2 ( D(i) The offset coefficiet is defied as the differece betwee the average ECG istace value i the rage block ad the average ECG istace value i the domai block.eq. (2) shows the calculatio of offset coefficiet[10]. O = 1 ( R(i) S D(i) ) (2) i=1 i=1 Eqs. (3) shows how to use scale ad offset coefficiets ad domai block to geerate the rage block[10]. R S D + O (3) These parameters are calculated for each rage block ad domai blockwhich eed to be compared ad describe the trasformatio relatioship betwee rage ad domai block. 151

3 The basic fractal model proposed i Ayma Ibaida s paper uses static compariso sequece, which meas each rage block eeds to compare with all domai blocks ad calculate the fractal coefficiets for all domai blocks. The compariso process is show i Fig. 1. Fig 1. The compariso process usig static sequece. I ECG sigal, two adjacet rage blocks are similar o the value of some parameters. So whe oe domai block is similar to a rage block greatly, it has a high possibility to be similar to the ext rage block. But this feature is ot used i the fractal model usig static compariso sequece which is show i Fig. 2. These domai blocks i the black boxes are more similar to the curret rage block obviously, but the fractal model usig static compariso sequece does t care about this feature ad it still compares the rage block with all domai blocks oe by oe. Compressio algorithm Fig 2. The defect of static compariso sequece. I our improved fractal model, dyamic compariso sequece is used to reduce the umber of compariso ad accelerate the compariso process. The compariso sequece of curret rage block is geerated by the compariso result of previous rage block. It ca always keep the more similar domai blocks i the frot of the compariso sequece for each rage block ad fid the domai block meetig the requiremet to break the iteratio without comparig with whole domai. The compariso process is show i Fig

4 Fig 3. The compariso process usig dyamic sequece. I the proposed improved fractal based compressio techique, for each rage block algorithm fids the domai block with high similarity. There is a queue storig the idexes of domai block. For each give rage block, the algorithm iterates through domai blocks accordig the idex order stored i the queue ad calculates the fractal coefficiets. Whe the curret domai block is similar to the give rage block greatly, algorithm keeps the correspodig idex i place. Whe the curret domai block is ot similar to the give rage block, algorithm moves the correspodig idex to the tail of the queue. After foud the domai block meetig requiremet, the idexes queue has bee adjusted ad ca be used as the compariso sequeceof the ext rage block. Fractal Root Mea Square (RMS) is used as the similarity measuremet betwee rage block ad domai block.eq. (4) shows the calculatio of the RMS[9]. RRRRRR = 1 [ RR(ii)2 + SS SS DD(ii) 2 2 RR(ii)DD(ii) + 2OO DD(ii) + OO( 2 RR(ii) )] If the curret RMS is less tha the previous stored value, algorithm will store the curret calculated fractal coefficiet i the output parameters ad update the RMS value. If the curret RMS is less tha some threshold, algorithm will break the curret iteratio i advace ad store the correspodig fractal coefficiets to the compressed file. I order to further improve the performace, some codig techiques ca be used.some arrays ca be calculated before the iteratio ad stored i the memory so that program ca ru faster with a little more memory usage. Meawhile, affie trasforms [11] are applied to help to achieve higher similarity betwee the rage ad domai blocks. Four differet kids of affie trasformatios are used i the algorithm ad the affie trasformatio ecodig umber will be store i the fial compressed file. The fial compressed file cotais several rows, each row icludes the fractal coefficiet (scale ad offset), the domai block idex ad the affie trasformatio ecodig umber. Compressio Algorithm INPUTS: R represets the origi ECG sigal bs represets the block size js represets the jump step of the search loop i domai OUTPUTS: so represets the scale value for the selected domai block oo represets the offset value for the selected domai block io represets the idex of the selected domai block (4) 153

5 aff0 represets the affie trasformatio ecodig value for the selected domai block // parameter iitial D=the dow-sampled versio of origi ECG sigal umofrblocks=the umber of rage blocks umofdblocks=the umber of domai blocks queue=oe-dimesioal queue, queue[i] represets the idex of domai block q=0, represets idex of queue // queue iitial while (q< umofdblocks) queue.add(q++) for each rage block Ri i R do: sumr=sum(ri) sumr2=sum(ri.^ 2) rms0=1000 so=0 oo=0 io=0 aff0=0 =bs toappedlist=oe-dimesioal queue storig the elemet reomved from queue for each elemet q i queue do: j=queue[q] for a=0 to 1 do: Dj=jth domai block sumrd=sum(ri * Dj) sumd=sum(dj) sumd2=sum(dj.^ 2) s=(( * sumrd) - (sumr * sumd[j])) / ( * sumd2[j] - sumd[j]^2) s=(sumr - s * sumd[j]) / rms=sqrt((sumr2 + s * (s * sumd2[j] - 2 * sumrd + 2 * o * sumd[j]) + o * ( * o - 2 * sumr)) / ) if rms<rms0: so = s oo = o io = j aff0 = a rms0 = rms ed if ed for if rms0<5.75 do: break ed if if rms0>15 do: remove q from queue add q to toappedlist ed if ed for add toappedlist to queue write so, oo, io, aff0 to compressd file ed for 154

6 Evaluatio Three measuremets are used i this paper to measure theperformace of the proposed improved fractal model ad compare it with the basic fractal model.the compressio ratio (CR) is a very importat measuremet that reflects the ratio betwee the origial sigal ad the compressed sigal. Eq. (5) shows the calculatio of the compressio ratio. tthee ssssssss oooo oooooooooooooooo ffffffff CCCC = (5) tthee ssssssss oooo cccccccccccccccccccc ffffffff The percetage residual differece (PRD) is a importat measure that reflects the differeces betwee the origial sigal ad the recostructed sigal. Eq. (6) shows the calculatio of the percetage residual differece. PPPPPP = NN (RR ii RR rrrrrr ) 2 NN 2 RR ii R represets the origial ECG sigal ad R re represets the recostructed versio. The improved fractal model based algorithm is measured usig the MIT-BIH Arrhythmia Database. Each ECG record is of 30 mi legth ad collected from differet patiets. Due to the limitatios of our equipmet, the test for the improved fractal model i this paper just use 10 secods of each record. If we use loger legth data i the future work, the test result will be better (the value of PRD will be lower). However, eve i the curret situatio, the improved fractal model still achieve good performace. I the improved fractal mode,the block size used is 35 poits ad the jump step is 10 poits.the model ad the algorithm are implemeted by Java laguage ad experimets are executed o the retia MacBook Prowith Mac OS X system. The experimet result ad the performace of the basic model ad other ECG compressio techiques are show i Table 1. The proposed algorithm ca achieve the compressio ratio of 42 with the PRD value less tha 2%. I light of the fact that the similarity with the origial data becomes meaigless whe the PRD value is higher tha 2% [5]. Compared with the basic fractal model, the improved model ca achieve same compressio ratio ad similar PRD error. Table 1 CR ad PRD for differet compressio techiques compared with ours. The improved Data model The basic model[9] [5] [6] [7] [8] CR PRD CR PRD CR PRD CR PRD CR PRD CR PRD (6) 155

7 The compressio time compariso betwee the basic fractal model ad the improved fractal model is show i Table 2 ad Table 3.The legth of the ECG segmet used i the experimet is 10 secods.the uit is millisecod. I this paper, the basic model is implemeted by ourselves accordig to the correspodig paper [9]. Both models use the block size of 35 ad jump step of 10 ad ruo the same machie. As the tables show, the executio time of the improved model ca be faster 4 times tha the basic model. Table 2 Executio time compariso of basic model ad improved model Data The improved model The basic model Table 3 Executio time compariso of basic model ad improved model Data The improved model The basic model Coclusio I this paper, a improved faster fractal model based ECG compressio techique is proposed to reduce the executio time of the basic model. The fractal model has bee proved that ca be used to be a good ECG compressio techique with high compressio ratio ad low PRD error. However, the high computatio complexity ad log executio time makes the basic fractal model be difficult to used i large-scale applicatios. Dyamic sequece techique is used i this paper to optimize the compariso process of the rage ad domai blocks. Fially,the proposed faster fractal model ca achieve same compressio ratio ad similar PRD error with oly ¼ executio time of the basic model. It is possible to reduce the PRD error further which will be studied i the future work. Refereces [1] Aravut Z. ECG sigal compressio based o Burrows-Wheeler trasformatio ad iversio raks of liear predictio[j]. Biomedical Egieerig, IEEE Trasactios o, 2007, 54(3): [2] Fira C M, Goras L. A ECG sigals compressio method ad its validatio usig NNs[J]. Biomedical Egieerig, IEEE Trasactios o, 2008, 55(4): [3] Huag B, Wag Y, Che J. 2-D compressio of ECG sigals usig ROI mask ad coditioal etropy codig[j]. IEEE trasactios o bio-medical egieerig, 2009, 56(4): [4] Ku C T, Hug K C, Wu T C, et al. Wavelet-based ECG data compressio system with liear quality cotrol scheme[j]. Biomedical Egieerig, IEEE Trasactios o, 2010, 57(6): [5] S. Lee, J. Kim, M. Lee, A real-time ECG data compressio ad trasmissio algorithm for a e- health device, IEEE Tras. Biomed. Eg. 58 (9) (2011) [6] N.Rodrigues,E.daSilva,S.deFaria,V.daSilva,M.deCarvalho,etal.,ECGsigal compressio based o DC equalizatio ad complexity sortig, IEEE Tras. Biomed. Eg. 55 (7) (2008) [7] H.-H. Chou, Y.-J. Che, Y.-C. Shiau, T. so Kuo, A effective ad efficiet compressio algorithm for ECG sigals with irregular periods, IEEE Tras. Biomed. Eg. 53 (6) (2006) [8]A. Khalaj, H.M. Naimi, New efficiet fractal based compressio method for electrocardiogram sigals, i: Caadia Coferece o Electrical ad Computer Egieerig, CCECE 09, IEEE, 2009, pp

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