低秩矩陣恢復的限制等距常數(shù)界.pdf

1、浙江大學博士學位論文低秩矩陣恢復的限制等距常數(shù)界姓名：王會敏申請學位級別：博士專業(yè)：應用數(shù)學指導教師：李松20120523AbstractInmanvrealapplicationsjithaSbeenshowninpracticethatVarioussignalsofinterestmaybe(approximately)sparselymodeledandthatsparsemodelingisoftenbeneficialAri

2、chtheoryofsparseandcompressiblesignalrecoVeryhasrecentlvbeendevelopedunderthenamescompressedsensingThisreVolutionaryresearchhasdemonstratedthatmanysignalscanberecoveredfromseVerelyun—dersampledmeasurementsbytakingadvanta

3、geoftheirinherentloⅥ乙dimensionalstructureA40rerecentl、r，anokshootofCShasbeenafocusofresearchmatricesoflowrankLo瓢一rankmatrixrecovery(LRMR)isdemonstratingarapidlygrowingarrayofimportantapplicationssuchaLSquantumstatetomogr

4、aphHrecommendersystemsandsystemidenti6cationandcontr01Inthispaper，we6rstdiscussedtheproblemthatrecoVersignalswithpartialsupportknown、^絕f6cusonthecasethattheknoⅥ，ninformationonsupportsetisexactandgavethesu伍cientconditionv

5、iaRIPtoguaranteetheexactrecoVeryanddiscussedthenoisvcaseOurresultsimprovedtheresultsin[701Nextweinvestigatedthetheoryoflowrankmatricesrecoveryasf01loⅥring：Givesomedecaypropertiesoftherestrictedisometryconstantsoflinearen

6、—semble：Providetheupperboundsofrestrictedisometryconstantstoguaranteetheexactrecoveryf6rloⅥtrankmatricesandthestabilit)’analysis1、7％proVedthatif62r≥_去or6r≥；，thenthereexistsomematrixwithrankatmostrV‘uwhichcannotbeexactlyr

7、ecoVeredbynuclearnormminimizationImprovetheboundsofrestrictedisometryconstantsfbrthestabilitj’analysisforthematrixDantzigselectorandLassoalgorithmProvidetheboundsofrestrictedisometr)’constantstoguaranteetheloⅥ’rankmatric