matlab大学外文资料翻译 学位论文.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