方向多分辨圖像變換及其應(yīng)用.pdf

1、中國科學(xué)技術(shù)大學(xué)碩士學(xué)位論文方向多分辨圖像變換及其應(yīng)用姓名：章鵬申請學(xué)位級別：碩士專業(yè)：信號與信息處理指導(dǎo)教師：倪林20060501AbstractMultiscaleGeometricAnalysisisaboominghotresearchtopicinrecentyearswhichaimstoobtainflexible，fastandeffectivesignalprocessingalgorithmsthrougheffic

2、ientmultiscaleapproximationandcharacterizationfortheinherentgeometricstructuresofhighdimensionaldataWhileCurveletandContourlet，asitstwo—dimensionalcases，representatypeofnewharmonictransformsarmedwithmultiresolution，local

3、ity，directionalityandanisotropyTheworkofthisthesisismainlyonthedesignandimplementationofbothCurveletandContourletandalsotheirapplicationsTheyareconcretelyasfollows：DiscretesymmetriclocalFourierbasisforfinitelengthsignal，

4、andalsoitsfoldandunfoldformulaforafastalgorithmofthesameorderasFFTarepresentedhere，AfterprovingtheequalitybetweenMeyerwaveletandsymmetriclocalFourierbasis，thethesisoffers，forsignalofarbitrarylength，anorthogonalwavelet—li

5、kedecompositionthatisessentiallyanearlydyadicpartitionoffrequencyaxisbysymmetriclocalFourierbasisThenFiniteRidgelettransformisimprovedbythewaveletlikedecompositionandisusedforanewlowredundancycurvelettransfotinThedesigna

6、ndimplementationforContourletsofdifferentredundancyarealsostudiedAtfirst，adesignmethodispresentedforoptimalFIRtwo—channelnonsubsampledfilterbank(FB)oflinearphaseandperfectreconstruction(PR)，anditisusedfortheoptimaldesign

7、ofnonsubsampledContourlet洲SCT)Infact，thedesignedFBhasabestfrequencyqualityandanearlypseudo—inversereconstructionDuetothehighredundancyofNSCTthreecombinableschemesareintroducedtocomputationalefficiencyofNSCTbasedonitsdesi

8、gnprocedureandFBstructure，andtheyareliftingstructure，polyphasestructureand1DseparableconvolutionThenthethesisexploresdeeplytheimplementationofpolyphasestructureinperiodicconvolutioncaseandfindsasolutionforimageofdyadicsi

9、zeAtlast，afterprovingapropositiontoincreasetheredundancyofPRFB，flexibleredundantContourletsarepresentedDistortiondenoisingisproposedasageneralizationoftranslationinvariantdenoising，thenShearingandrotatingareintroducedast

10、woeffectivedistortionschemestemedythedeficiencyoftransformdirectionalityAnewofbandlimitedinterpolationalgorithmisproposedfortheimplementationofshearingandrotatingdistortionFinallyContourletsareusedintextureimageretrieval