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Thetraditionalsignaltheory,isbuiltonthebasisoftheanalysisofFourier,Fouriertransformisakindofglobalchange,ithassomelimitations.Inpracticalapplication,thepeoplestarttoFouriertransformareimproved,thusresultinginwaveletanalysis.Waveletanalysisisanewbranchofmathematics,itisauniversalfunction,Fourieranalysis,harmonicanalysis,numericalanalysisofthemostperfectcrystalline;
inthefieldsofapplication,especiallyinsignalprocessing,imageprocessing,speechprocessingandnonlinearsciencedomain,itisconsideredtobetheFourieranalysisafteranothereffectivewhenfrequencyanalysismethod.WavelettransformandFouriertransform,isatimeandfrequencydomainofthelocaltransformwhichcaneffectivelyextractedfromthesignalinformation,throughdilationandshiftoperationfunctiontofunctionorsignalmultiscaleanalysis(MultiscaleAnalysis),tosolvetheFouriertransformcannotsolvemanydifficultproblems
Wavelettransformisarapiddevelopmentandmorepopularsignalanalysismethod,theimageprocessingisaveryimportantapplication,includingimagecompression,imagedenoising,imagefusion,imagedecomposition,imageenhancement.Waveletanalysisistheanalysismethodofthinkinginthedevelopmentandcontinuation.Inadditiontocontinuouswavelet,discretewavelettransform(CWT)(DWT),andthewaveletpacket(WaveletPacket)andmultidimensionalwavelet
Waveletanalysisinimageprocessingapplicationsareveryimportant,includingimagecompression,imagedenoising,imagefusion,imagedecomposition,imageenhancement.Wavelettransformisanewtransformanalysismethod,ithasinheritedanddevelopedtheSTFTlocalizationofthought,andalsoovercomesthewindowsizedoesnotvarywithfrequencyandothershortcomings,toprovideafrequencychangingwithtimefrequencywindow,isatime-frequencysignalanalysisandprocessingtheidealtool.Itismainlycharacterizedbytransformcanhighlightsomeaspectsofcharacteristics,therefore,thewavelettransforminmanyareashavebeensuccessfullyapplied,especiallywavelettransformdiscretedigitalalgorithmhasbeenwidelyusedinmanyoftheproblemsofthetransformationresearch.Sincethen,thewavelettransformismoreandmoretheintroductionofpeople'
sattention,itsapplicationfieldsmoreandmorewidely.
2,problemoverview
(a)theapplicationofwaveletanalysisanddevelopment
Theapplicationofwaveletanalysisandwaveletanalysistheorytoworkcloselytogether.Now,ithasbeenintheinformationtechnologyindustryhasmadetheachievementattractpeople'
sattention.Electronicinformationtechnologyisthesixnewandhightechnologyanimportantfield,whichisanimportantaspectofimageandsignalprocessing.Nowadays,signalprocessinghasbecomeanimportantpartoftheworkofcontemporaryscienceandtechnology,thepurposeofsignalprocessingis:
accurateanalysis,diagnosis,codingandquantization,fasttransmissionorstorage,accuratelyreconstruct(orreturn).Fromamathematicalperspective,signalandimageprocessingcanbeunifiedasaletter
Coursenumberprocessing(imagecanbeviewedasatwo-dimensionalsignal),thewaveletanalysisofthemanyanalysisformanyapplications,canbeattributedtothesignalprocessingproblems.Now,foritspropertieswithtimestablesignal(stationaryrandomprocess),anidealtoolinprocessingisstillaFourieranalysis.Butinthepracticalapplicationofthevastmajorityofsignalisunstable(nonstationaryrandomprocess),andisespeciallysuitablefortheunstablesignalwaveletanalysistoolis.
Infactthewaveletanalysisappliedfieldisveryextensive,itincludesmanydisciplines:
mathematics;
signalanalysis,imageprocessing;
quantummechanics,theoreticalphysics;
militaryelectronicwarfareandweaponscomputerintelligent;
classificationandrecognition;
musicandlanguageartificialsynthesis;
medicalimaginganddiagnosis;
seismicdataprocessing;
mechanicalthefaultdiagnosisandsoon;
forexample,inmathematics,ithasbeenusedinnumericalanalysis,structure,fastnumericalmethodofcurveandsurfacestructure,solvingdifferentialequations,controltheory.Insignalanalysis,noisefiltering,compression,transmissionandsoon.Intheimageprocessingoftheimagecompression,classification,identificationanddiagnosis,suchasthedecontamination.Inmedicalimaging,thereductionofBultrasound,CTnuclearmagneticresonanceimagingtime,improvetheresolution
(1)applicationofwaveletanalysisinsignalandimagecompressionwaveletanalysisisanimportantapplicationofthe.Itischaracterizedbyhighcompressionratio,compressionspeed,thecompressedsignalcanbemaintainedandimagefeatureinvariant,andthetransferofantiinterference.Thecompressionmethodbasedonwaveletanalysis,comparativesuccessofwaveletpacketbestbasemethod,wavelettexturemodelmethod,wavelettransformZerotreecompression,wavelettransformvectorcompression.
(2)thewaveletinthesignalanalysisarewidelyused.Itcanbeusedforboundaryprocessingandfiltering,time-frequencyanalysis,signal-noiseseparationandextractionofweaksignal,fractalindex,signalrecognitionanddiagnosisaswellasthemulti-scaleedgedetection.
Inconclusion,becausewavelethaslowentropy,multi-resolution,decorrelation,selectedmediumcharacteristicssuchasflexibility,thetheoryofwaveletindenoisingfieldsbymanyscholars,andobtainedgoodresults.Buthowtotakecertaintechnologytoeliminateimagenoisewhilepreservingimagedetailisanimportanttopicintheimagepretreatment.Atpresent,basedonwaveletanalysisinimagedenoisingimagedenoisingtechnologyhasbecomeanimportantmethod.
(b)intheimageprocessingfield,wavelettransformhasthefollowingadvantages:
(1)waveletdecompositioncancoverthewholefrequencydomain(providesamathematicallycompletedescription)
(2)wavelettransformbyselectingappropriatefilter,cangreatlyreduceorremovethecorrelationbetweendifferentfeatureextraction
(3)wavelettransformhasa"
zoom"
characteristics,inthelowfrequencybandcanbeusedwithhighfrequencyresolutionandlowresolution(widthanalysiswindow),inthehighfrequencyband,theavailablelowfrequencyresolutionandhightemporalresolution(narrowanalysiswindow)
(4)wavelettransformonafastalgorithm(Mallatalgorithm)Waveletanalysishasbecomeoneofthefastestandmostattractsb.'
sattentionononeofthesubjects,orappliedtothefieldofinformationinvolvedinalmostalldisciplines.
(c)demonstrationprogram
Thispaperbasedonthewavelettransformimagedenoisingmethodscarriedoutin-depthresearchandanalysis,thepaperintroducesseveralclassicwavelettransformdenoisingmethod.Thewavelettransformmodulusmaximumdenoisingmethod,describedindetailthedenoisingprincipleandalgorithm,analyzesthedenoisingprocessparameterselectionproblem,andgivessomebasis;
detailedcorrelationofwaveletcoefficientdenoisingmethodprincipleandalgorithm;
wavelettransformthresholddenoisingmethodprincipleandseveralkeytheproblemisdiscussedindetail.Thelastofthesemethodsareanalyzedandcompared,anddiscussestheirrespectiveadvantagesanddisadvantagesandapplicableconditions,andgivesthesimulationresults.
Inmanyimagedenoisingbasedonwavelettransformmethod,isthelargestusewaveletshrinkagedenoisingmethod.Thetraditionalhardthresholdfunctionandsoftthresholdfunctionde-noisingmethodinpracticehasbeenwidelyused,andachievedgoodresults.ButthehardthresholdfunctionisdiscontinuousresultingreconstructedsignalpronetofalsephenomenonofGibbs;
andthesoftthresholdfunctionalthoughtheoverallgoodcontinuity,buttheestimatedvalueandtheactualvalueofaggregateinthepresenceofconstantdeviation,withcertainlimitations.Inviewofthis,thispaperputsforwardamethodbasedonwaveletmultiresolutionanalysisandminimummeansquareerrorcriterionforadaptivethresholddenoisingalgorithm.Themethoduseswaveletthresholdde-noisingprinciple,basedonminimummeansquareerroralgorithmofLMSandSteinunbiasedestimatesofthepremise,thederivationofacontinuousderivativewithmultiplethresholdfunction,theuseofthethresholdforiterativeoperation,gettheoptimalthreshold,resultinginbetterimagedenoisingeffect.Finally,thesimulationresultscanbeseen,thedenoisingeffectisremarkable,andhardthreshold,softthresholdmethodiscompared,theSNRimprovementmore,atthesametimedenoisingcanpreserveimagedetails,isaneffectivemethodforimagedenoising.
Waveletbasisfunctionfromthefollowing3aspectstoconsider.
(1)complexandrealwaveletselectionComplexwaveletanalysiscannotonlyobtaintheamplitudeinformation,canalsobeobtainedfromthephaseinformation,sothecomplexwavele