基于小波变换的图像降噪

X(,354300),,,,,;,;;:TN911.73:A:1008-5963(2006)04-0067-04ImageNoiseReductionBasedonWaveletTransformCUIXiarong(ElectronicEngineeringDepartmentofNanpingTeachersCollege,Wuyishan354300,China)AbstractAccordingtothecharacteristicofenergydistributionofwavelettransformandnoise,amethodofimagenoisereductionisproposed.Firstly,noisedimageisdecomposedbywavelettransformwithmorescale.Secondly,thesquaremarginofnoiseandthresholdinhighfrequencycoefficientsofwavelettransformwithdifferentscalearefiguredout.Andthecoefficientsaredealtwithdifferentthreshold.Finally,reconstructedimagecanbeobtainedbyusinginversewavelettransformforallcoeffi2cients.Experimentalresultsprovethatbyusingthismethod,imagenoisecanbereducedeffectivelyandimagedetailscanbepreservedalot.Keywordswavelettransform;threshold;imagedenoising1,,,,,,,,,,,,,,,,,,,2,(x,y)f(x,y),(x,y)f(x,y),[1](x,y),:(x,y)=(x)(y)(1)31(x,y)=(x)(y),2(x,y)=(x)(y),3(x,y)=(x)(y)(2),(x)(y)(x)(y)3ij,m,n(x,y)=2-ji(2-jx-m,2-jy-n),j,m,nz,i=1,2,3(3)76X:2006-09-08:(XQL05012):(1965-),,,,,:254Vol.25No.4200610JOURNALOFNANPINGTEACHERSCOLLEGEOct.2006©1994-2007ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.(x,y),L2(R2),Mallat,{j-1,m,n(x,y);m,nz}:span[j-1,m,n(x,y);m,nz]=span[j,m,n(x,y);m,nz]Ýspan[ij,m,n(x,y);i=1,2,3;m,nz](4)f(x,y)2j()Dj(m,n)Dj(m,n)=f(x,y),j,m,n(x,y)=2-j[f(x,y)3j(-x)j(-y)](2jm,2jn),m,nz(5)j(x)=2-j(2-jx-m),j(y)=2-j(2-jy-n);f(x,y)2j()3C1j(m,n)=f(x,y),1j,m,n(x,y)=2-j[f(x,y)3j(-x)j(-y)](2jm,2jn),m,nz(6)C2j(m,n)=2-j[f(x,y)3j(-x)j(-y)](2jm,2jn),m,nz(7)C3j(m,n)=2-j[f(x,y)3j(-x)j(-y)](2jm,2jn),m,nz(8),f(x,y)xy,,f(x,y)j(-x),,j(-y),,C1j(m,n)Dj(m,n),C2j(m,n),C3j(m,n)Dj(m,n)j,C1j(m,n),C2j(m,n),C3j(m,n)()f(x,y)=Jj=1imnCijij,m,m(x,y)+mnj,m,m(x,y)(9)(22881712,JPG),(1)j=2,(2);LL,HL,LH,HH33.11992MallatLipschitz,[4]:f(t)Lipschitza0,f(t),f(t)Lips2chitza0,f(t)Lipschitza0,Lipschitza0,,,,1j=22f(x,y)=s(x,y)+z(x,y)(3-1)8620064©1994-2007ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.(x,y),z(x,y)F(x,y)=S(x,y)+Z(x,y)(3-2)Mallat,f(x,y),s(x,y)Cij(m,n)(i=1,2,3LH,HL,HH),,;z(x,y)Cij(m,n),,,Cij(m,n);Dj(m,n),Dj(m,n)Dj(m,n)Cij(m,n),3.2,,Donoho,[23](1)(HardThresholding),T;:Y=X|X|T0|X|T(3-1)(2)(SoftThresholding):Y=sgn(X)f(|X|-T)|X|T0|X|T(3-2)T,(3-3):=median(abs(cd))0.6745(3-3)median,cdT:T=2ln(N)(3-4)N,Gibbs;,;T,,Birge-MassartBirge-MassartT:crit(t)=-C2(k)+22t(+log(n/t))kt(3-5)c(k),n,,23.396:©1994-2007ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.(3),sym4,N=3,TBirge-Massart,T(),,(4)(4)(a);(b);(c)(d)(e)j=123,;(f)j=1,(c)(d)(e)(f),,(a);,,Gibbs44,,,,,,?[1],.[M].,2002:282285.[2].[M].,2003:152159.[3]DonohoDL.De-noisingbySoft-thresholding[J].IEEETransonInformationTheory,1995,41(3):613627.[4]MallatS,HwangWL.SingularityDetectionandProcessingwithWavelets[J].IEEETrans.Info.Theory,1992,38(2):617643.0720064©1994-2007ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.