多元向量值分叉連分式插值的構(gòu)造和在圖像縮放中的應(yīng)用.pdf

1、H#號(hào)j絲些』镕a：——學(xué)號(hào)：啦業(yè)墜坐!咝26侖肥工學(xué)大警HefeiUniversityofTechnology碩士學(xué)位論文MASTERDISSERTATIoNo論文題目：多元向量值分叉連分式插值的構(gòu)造學(xué)位類別：學(xué)科專業(yè)：(工程領(lǐng)域作者姓名導(dǎo)師姓名：焦魚鏖墼塑完成時(shí)間TheConstructionofVectorValuedInterpolantsbyMultibranchedContinuedFractionsandApplicati

2、onsintheImageZoomingAbstractVectorvaluedrationalinterpolation(ievectorrationalinterpolation，hereinafter)issuewasproposedbyWynnin1963，whenhenoticedthatbyadopting8algorithmandimplementingSamelsoninverseonavectoronecouldobt

3、ainthesameaccurateresultasthescalarmethoddidSince1983，GravesMorrishasdonesomeresearchaboutunivariatevectorvaluedrationalinterpolationunderpracticalapplicationbackground(suchasmachinevibrationdataanalysisandSOforth)andest

4、ablishedafewmethodsaboutinterpolationVectorvaluedrationalinterpolationisnowextendedtosomecasesinwhichmultiplevariablesareinvolvedandsomesignificantresultsareobtainedAsfortheimagezooming，thefollowinginterpolationmethodsar

5、eusuallyadopted：(1)nearestneighborhoodinterpolation；(2)bilinearinterpolation；(3)cubicB—splineinterpolation；(4)generalbicubicsplineinterpolation；(5)adaptiveinterpolation；(6)waveletinterpolation；(7)fractalinterpolationThef

6、irstfourinterpolationmethodsaredevelopedfullyandhavebeenappliedtomanyimageprocessingsofiwares，whiletheremaindersbearsomeshortcomingsandcallforfurtherinvestigationInthisthesis，wefocusourattentiononintroducingthemethodsand

7、theoryrelatedtomultivariatevectorvaluedbranchedcontinuedfractions，andprovidingcorrespondingconstructionmethodandcharacteristictheoremonthebasisofprincipaltheoryofcontinuedfractionsFinally，Weapplythebivariatevectorvaluedr

8、ationalinterpolationtOtheimagezoomingsuccessfullyThemethodpresentedinthisthesishasconsiderablemeritsinreservingthesharpnessoftheimageKeywords：vectorvaluedfunction，rationalinterpolation，branchedcontinuedfractions，imagezoo