Application of Wavelet Transform in MCG-signal Denoising
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1 Appliction o Wvelet Trnsorm in MCG-signl Denoising Yuci Dong, Hongto Shi, Junzhi Luo, Gehu Fn & Ciping Zhng Institute o Nonliner Science, Acdemy o Armored Force Engineering, Beijing 17, Chin Abstrct In this pper, the principle o denoising ith velet trnsorm re discussed. The ppliction o velet threshold denoising method in MCG-signl processing problem is introduced. Progrm is ritten by MATLAB to relize velet threshold denoising method. The results sho tht the velet threshold denoising method in the MCG-signl denoising cn not only restrin the noise eectively, but lso reserve the ult chrcter inormtion in the originl signl. The signls by this method re better improvements thn trditionl method. Keyords: MCG-signl, Wvelet Trnsorm, Signl Denoising 1. Introduction With the continuous development o biomgnetism detection technology, the method o Mgneto Crdio Grphy hs been pplied to the stge o clinicl ppliction ith the dvntges o non-trumtic, non-contct, highly sensitive, non-rditive nd so on. The Mgneto Crdio Grphy, using SQUID s the detecting devices to detect nd nlyze the MCG-signl, is highly sensitive detecting equipment hich detect nd dignose the hert disese. Ho to denoise is the ey to detect MCG-signl becuse the MCG-signl o humn beings is very int hich is only one prt per million o geomgnetic ield.(chen, Lin. 6) (zhng, xiyun. ) nlyze nd reserch noise cncelltion bout the MCG-signl ming use o ourier trnsorm method, hich remove the eect o noises to some extent. (Hu, Rong. 5) pplied the mthemticl morphologicl iltering method to nlyze nd process the MCG-signl nd the resulting tests sho tht this method cn eliminte rndom nd high requency noise eectively, but the disdvntge is the selection o structurl elements ects the resulting test very much. (Wng, ei. 8) pplied the morphologicl iltering method to construct to inds o structurl elements, hich cn preserve the component o T ve in the MCG-signl nd lso remove the bseline drit o the MCG-signl. This pper mes use o velet trnsorm to nlyze nd process noise cncelltion bout the MCG-signl in the vie o mthemtics. The resulting tests revels tht this method is eective hich my not only remove rndom nd high requency noise but lso preserve the signl.. The principle o velet trnsormtion The velet trnsorm is n nlyzing method hving good loclly etures in both time domin nd requency domin. The velet trnsorm dopts grdully precise sptil domin step to process high requency, so it cn ocus on optionl detils o the nlyzed trget, hich ords ne processing method or the signl process. Hoever, the trditionl ourier trnsorm hich completely nlyzes signls in the requency domin hs no resolution or the signls in the time domin.(ji, Mingto & Wng, Yongchen. 3) The concept o the velet trnsorm is: the bsic velet unction ϕ is trnslted nd expnded to obtin one unction mily. (Li, Bicheng & Luo, Jinshu. 5) 1 x b ϕ, b ( x) = ϕ( ), (, b R, ) Where is the expnsion ctor nd b is the trnsltion ctor. Anlyze the signl through ming inner product ith the unction mily nd the signl. The velet unction should stisy to conditions: 1 ϕ is continul nd ttenution; the integrl o ϕ is zero. When the velet unction is determined, the continul velet trnsorm nd inverse trnsorm o the signl (t) re: 1 t b W (, b) ( t) ϕ ( ) dt = R 1 1 t b ( t) = W b ddb C ( ) (, ) ϕ ϕ RR
2 Vol., No. 6; June 1 here ˆ( ϕ ω) C ϕ = dω, ϕ (t) denotes the complex conjugte o ϕ (t) nd ϕˆ denotes the ourier ω R trnsormtion o ϕ. In the prcticl ppliction, e commonly dopt discrete velet trnsorm nd the deinition is: j j D ( ) = ( t) ϕ ( t ) dt R Where re the discrete numbers o the expnsion ctor nd the trnsltion ctor b, seprtely. 3. The ppliction o velet trnsorm in signl denoising Generlly speing ll the prcticl signls re signls ith noise, or exmple, ll inds o physiologicl electricl signls including crdic electricity, brin electricity nd gstric electricity in the biomedicine nd some other non-physiologicl electricl signls (s pulse ve, MCG et l.) hich re trnsormed to electricl signls re submerged in the strong noises resulting in losing the vlues o medicl dignosis. So noise cncelltion nd iltering re the importnt content o processing biomedicl signls. The trditionl method is tht one seprtes the signls nd noises ccording to the dierent requency bnds o signl nd noise, hich dopts the ourier trnsormtion to trnsorm the time domin to the requency domin. When the requency bnds o signls nd noises overlp, the eects o this method ill decrese pprently nd the contrdiction beteen protecting the locl eture o signls nd restrining noises exists. The velet trnsorm hs good qulity o time-requency locliztion, hich ord poerul tool or solving this problem. No, the velet technique is idely studied in the signl denoising nd obtins very good ppliction eect. The milir bsic methods o velet denoising re: module mximum o velet trnsorm denoising, noise cncelltion bsed the scle coherency o velet trnsorm nd velet threshold denoising. 3.1 module mximum o velet trnsorm denoising The module mximums o signls nd noises in the seprte scle o velet trnsorm hve completely dierent trveling chrcteristics. The Lipschitz exponents o common signls re usully more thn zero nd the number o module mximums is identicl in smller scle. Hoever, the Lipschitz exponents o noises re usully less thn zero. For exmple, the hite Gussin noise is distributing rndomly ith lmost singulr everyhere, hich hs negtive Lipschitz exponents. One cn observe the grdully chnging l o module mximums o velet trnsorm nd the distributing l o module mximums in dierent scles to estimte the loction o singulr points nd the corresponding Lipschitz exponents, hich cn seprte signls nd noises to relize velet denoising. This method depends on the noises little, hich does not need the vrince o noises, so it suits signl denoising ith lo S/N. Hoever, the clcultion ccurcy is lo nd the eects o noise cncelltion cn not be stisied. 3. noise cncelltion bsed the scle coherency o velet trnsorm The dierent spreding chrcteristics o the velet trnsorms o signls nd noises in dierent scles sho tht the velet trnsorm o signls hs strong coherency beteen dierent scles nd the coherency in mrgin is very strong, hoever, the velet trnsorm o noises does not hve the obvious coherency in dierent scles nd the velet trnsorm o noises minly ocus on dierent levels o smll scles. According to dierent chrcteristics o velet trnsorms o signls nd noises in dierent scles, one proposes the method ming use o the coherency o velet trnsorm to distinguish signls nd noises. This method cn obtin very good denoising eects nd the eects re stble, hich suits or the signls ith high S/N. The disdvntges re lrge mount o clcultion nd the requirement to evlute the vrince o noises. 3.3 Wvelet threshold denoising method The min theory o velet threshold denoising method is: the velet trnsorm, especilly the orthogonl velet trnsorm, hs strong denoising coherency, hich cn ocus the energy o signls included in the velet domin on some big velet coeicients nd distribute the energy o noises to ll the velet domin. Thereore, the mplitude o velet coeicient o signls is bigger thn tht o noises, so it cn be thought tht the velet coeicients ith bigger mplitude re minly signls nd the velet coeicients ith smller mplitude re noises to lrge extent. Thereore, the coeicients o signls re reserved nd most o coeicients o noises re reduced to zero using the threshold method. The velet threshold denoising method minly suits or signls mixed ith hite noises. The dvntges re highly clculting velocity, hose clcultion complexity is O (N) here N is the length o signl, nd the 1
3 noises re restrined lmost nd the chrcteristic plug points relecting the originl signls cn be reserved. The disdvntges re the denoising eects depend on S/N nd the choice o threshold hs very importnt inluences on the denoising eects. There re mny methods o choosing thresholds, nd the most common method is VisuShrin, hich dopts the globl uniorm threshold σ logn, here σ is the stndrd devition o noises nd N is the length o signls.. Noise cncelltion on MCG-signl pplying velet threshold denoising The MCG-signls re surveyed in the shielding room using high-tc squids. The dt re smpled ith the requency o 1 nd totl recording length o 5. The originl dt re shon s igure 1. Considering the requencies o MCG-signls minly concentrte belo 5HZ nd the MCG-signls re very int reltive to poer line intererence. So the dt should be preprocessed ith lo-pss ilter to eliminte poer line intererence nd high requency noises intererence, hich re shon s igure. From the igure, it is ound tht the MCG-signls include lrge mount o rndom noises intererence ter the trditionl lo-pss ilter processing nd these signl dt hve no prcticl mening or the clinicl dignosing, rom hich the rndom intererences hve to be eliminted or the uture nlyticl processing. The processed signls re denoised by pplying velet threshold denoising. The idiogrphic stges re: (1) The signls re decomposed by velet in ll the scles nd ll the velet coeicients in the condition o lo resolution nd lrge scles re preserved. In the process o decomposition, choosing the pproprite velet nd resonble decomposing lyers re very importnt or the denoising results. Figure 3 chooses the sym unction nd the number o decomposing lyers is 5. () The velet coeicients in ll the scles re processed by sot threshold. For eeping the hole igure o signls constnt, ll the lo requency coeicients re preserved. We ssume the threshold λ= σ log N, nd every velet coeicient is processed by pplying sot threshold. ~ = λ + λ λ < λ λ In the prcticl clcultion, ll the vrinces o noises re unnon, hich usully hve to be estimted. Becuse the noises minly ocus on the most high resolution grde J -1, the stndrd devitions o noises re estimted by using velet coeicients.(sun, Ynui. 5) (3) The processed velet coeicients re reconstructed ming use o inverse velet trnsorm to rene the eective signls, hich is shon in igure 3. Compring igure 3 ith igure, it is ound tht the velet trnsorm not only restrin noises but lso preserve the chrcteristic plug points relecting the originl signls, so it hs very good denoising eects.. Conclusions The velet trnsorm hs good resolution in both time domin nd requency domin, so it hs more dvntges in deling ith non-sttionry signls. This pper pplies the velet trnsorm in the process o denoising MCG-signls nd the results sho tht velet threshold denoising method not only elimintes the rndom noises o MCG-signls but lso gretly preserve the originl etures o signls. Reerences Chen, Lin. (6). Noise cncelltion techniques in mgneto crdio grphy bsed on velet pcet method. Chinese Journl o Lo Temperture Physics, 6,8():16~167. Hu, Rong. (5). A mthemticl morphologicl iltering pproch to remove the noise o MCG-signls. Modern Scientiic Instruments, 5,:5~55. Ji, Mingto & Wng, Yongchen. (3). Appliction o velet trnsormtion in signl processing or vibrting pltorm. Journl o Shenyng Institute o Technology, 3,(3):53~55. Li, Bicheng & Luo, Jinshu. (5). Wvelet nlysis nd its ppliction. Beijing: Electronic Industry Press, 5. Sun, Ynui. (5). Wvelet nlysis nd its ppliction. Beijing: Mechnicl Industry Press, 5.
4 Vol., No. 6; June 1 Wng, Wei. (8). Removl o the bseline drit in mgneto crdiogrm using the morphologicl ilter. Modern Scientiic Instruments, 8,1:93~95. Zhng, Yunxing. (). Anlysis o noise cncelltion techniques in mgneto crdio grphy bsed on ourier trnsorm method. Journl o Dlin College,,3(3):95~96. 1 x Figure 1. Signls surveyed originlly 6 x Figure. Signls eliminted poer line intererence 3
5 6 x Figure 3. Signls through velet trnsormed nd then iltered
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