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1、Subject:ResearchonImageRecoveryandFusionbasedonCompressedSensingSpecialty:SignalandInformationProcessingName:YanDi(Signature)Instructor:WuYanhai(Signature)ABSTRACTIntherapiddevelopmentofinformationtechnologyera,thetraditionalNyquistsamplingtheoryisunabletomeetthedemandforpracticalapplica
2、tion.RecentlyDonohoandCandesetc.proposethenewcompressedsensingtheorywhichpointsoutthatwhenthesignaliscompressibleorsparseinatransformdomain,afewrandomprojectionscontaintheenoughinformationofthesignaltoberecovered.Thesignalfinallycanbereconstructedfromtheseprojectionsbysolvinganoptimizati
3、onproblematthehighprobability.Thisnewtheoryhasafeatureofdirectlysamplinginformation.Thesamplingrate,whichisfarlowerthanNyquistsamplingrate,dependsontheinformationstructureandcontentofthesignalandcanmeasureandcodethesignal.Applicationsthatbenefitfromthenewtheoryconcludeimageprocessing,rad
4、arandsoon.Thispapermainlybringsthecompressedsensingtheoryintheimagerecoveryandfusion.Themaincontributionscanbesummarizedasfollows:(1)Themodifiedsubspacepursuitalgorithmisproposedtorecovertheimage.Thesubspacepursuitmusthavethepriorknowledgeofthesparsity,butinfactthesparsityofimagesisunkno
5、wn.Theproposedalgorithmadaptivelyestimatesthesparsityofsignals,whichestimatesthesparsityatthegivenstepfactorintheiterativeprocess.Whenthereconstructionerrorislessthanthethreshold,thenewalgorithmstopstheiterationandrealizestheaccuraterecoveryofsparsesignals.Thesimulationresultsshowthatcom
6、paredwithotheralgorithms,theproposedalgorithmhasadvantagesofthecomputationtimeandtheaccuracyofthereconstruction.(2)AnewalgorithmbasedonNSCTtransformisproposedtofusetheimages.Thewavelettransformmulti-directionallyminestheimagessothatitcann’tsparselyrepresenttheimagesverywell.Inthispaper,t
7、heNSCTtransformischosentosparselyrepresenttheimagesandthenewcompressedsensingtheoryisintroducedtomeasurethehigh-frequencycoefficients.Meanwhiletherules,maximizingthemeanofadjacentgradesandmaximizingthemeanofabsolutevariance,areadoptedtofusetheimagesbythehigh-frequencymeas