matlab大学外文资料翻译 学位论文Word文档格式.docx

matlab大学外文资料翻译 学位论文Word文档格式.docx

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matlab大学外文资料翻译学位论文@#@ComplexRidgeletsforImageDenoising@#@1Introduction@#@Wavelettransformshavebeensuccessfullyusedinmanyscientificfieldssuchasimagecompression,imagedenoising,signalprocessing,computergraphics,andpatternrecognition,tonameonlyafew.Donohoandhiscoworkerspioneeredawaveletdenoisingschemebyusingsoftthresholdingandhardthresholding.Thisapproachappearstobeagoodchoiceforanumberofapplications.Thisisbecauseawavelettransformcancompacttheenergyoftheimagetoonlyasmallnumberoflargecoefficientsandthemajorityofthewaveletcoeficientsareverysmallsothattheycanbesettozero.Thethresholdingofthewaveletcoeficientscanbedoneatonlythedetailwaveletdecompositionsubbands.Wekeepafewlowfrequencywaveletsubbandsuntouchedsothattheyarenotthresholded.ItiswellknownthatDonoho'@#@smethodofferstheadvantagesofsmoothnessandadaptation.However,asCoifman@#@andDonohopointedout,thisalgorithmexhibitsvisualartifacts:

@#@Gibbsphenomenaintheneighbourhoodofdiscontinuities.Therefore,theyproposeinatranslationinvariant（TI）denoisingschemetosuppresssuchartifactsbyaveragingoverthedenoisedsignalsofallcircularshifts.TheexperimentalresultsinconfirmthatsingleTIwaveletdenoisingperformsbetterthanthenon-TIcase.BuiandChenextendedthisTIschemetothemultiwaveletcaseandtheyfoundthatTImultiwaveletdenoisinggavebetterresultsthanTIsinglewaveletdenoising.CaiandSilvermanproposedathresholdingschemebytakingtheneighbourcoeficientsintoaccountTheirexperimentalresultsshowedapparentadvantagesoverthetraditionalterm-by-termwaveletdenoising.ChenandBuiextendedthisneighbouringwaveletthresholdingideatothemultiwaveletcase.Theyclaimedthatneighbourmultiwaveletdenoisingoutperformsneighboursinglewaveletdenoisingforsomestandardtestsignalsandreal-lifeimages.Chenetal.proposedanimagedenoisingschemebyconsideringasquareneighbourhoodinthewaveletdomain.Chenetal.alsotriedtocustomizethewavelet_lterandthethresholdforimagedenoising.Experimentalresultsshowthatthesetwomethodsproducebetterdenoisingresults.Theridgelettransformwasdevelopedoverseveralyearstobreakthelimitationsofthewavelettransform.The2Dwavelettransformofimagesproduceslargewaveletcoeficientsateveryscaleofthedecomposition.Withsomanylargecoe_cients,thedenoisingofnoisyimagesfacesalotofdiffculties.Weknowthattheridgelettransformhasbeensuccessfullyusedtoanalyzedigitalimages.Unlikewavelettransforms,theridgelettransformprocessesdatabyfirstcomputingintegralsoverdifferentorientationsandlocations.Aridgeletisconstant@#@alongthelinesx1cos_+x2sin_=constant.Inthedirectionorthogonaltotheseridgesitisawavelet.Ridgeletshavebeensuccessfullyappliedinimagedenoisingrecently.Inthispaper,wecombinethedual-treecomplexwaveletintheridgelettransformandapplyittoimagedenoising.Theapproximateshiftinvariancepropertyofthedual-treecomplexwaveletandthegoodpropertyoftheridgeletmakeourmethodaverygoodmethodforimagedenoising.Experimentalresultsshowthatbyusingdual-treecomplexridgelets,ouralgorithmsobtainhigherPeakSignaltoNoiseRatio（PSNR）forallthedenoisedimageswithdi_erentnoiselevels.Theorganizationofthispaperisasfollows.InSection2,weexplainhowtoincorporatethedual-tree@#@complexwaveletsintotheridgelettransformforimagedenoising.ExperimentalresultsareconductedinSection3.Finallywegivetheconclusionandfutureworktobedoneinsection4.@#@2ImageDenoisingbyusingComplex@#@RidgeletsDiscreteridgelettransformprovidesnear-idealsparsityofrepresentationofbothsmoothobjectsandofobjectswithedges.Itisanear-optimalmethodofdenoisingforGaussiannoise.Theridgelettransformcancompresstheenergyoftheimageintoasmallernumberofridgeletcoe_cients.Ontheotherhand,thewavelettransformproducesmanylargewaveletcoe_cientsontheedgesoneveryscaleofthe2Dwaveletdecomposition.Thismeansthatmanywaveletcoe_cientsareneededinordertoreconstructtheedgesintheimage.WeknowthatapproximateRadontransformsfordigitaldatacanbebasedondiscretefastFouriertransform.Theordinaryridgelettransformcanbeachievedasfollows:

@#@@#@1.Computethe2DFFToftheimage.@#@2.SubstitutethesampledvaluesoftheFouriertransformobtainedonthesquarelatticewithsampledvaluesonapolarlattice.@#@3.Computethe1DinverseFFToneachangularline.@#@4.Performthe1Dscalarwavelettransformontheresultingangularlinesinordertoobtaintheridgeletcoe_cients.@#@Itiswellknownthattheordinarydiscretewavelettransformisnotshiftinvariantbecauseofthedecimationoperationduringthetransform.Asmallshiftinthein