Topics in Compressed Sensing

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1、TopicsinCompressedSensingByDeannaNeedellB.S.(UniversityofNevada,Reno)2003M.A.(UniversityofCalifornia,Davis)2005DISSERTATIONSubmittedinpartialsatisfactionoftherequirementsforthedegreeofDOCTOROFPHILOSOPHYinMATHEMATICSintheOFFICEOFGRADUATESTUDIESoftheUNIVERSITYO

2、FCALIFORNIADAVISApproved:RomanVershyninRomanVershynin(Co-Chair)arXiv:0905.4482v1[math.NA]27May2009ThomasStrohmerThomasStrohmer(Co-Chair)Jes´usDeLoeraJes´usDeLoeraCommitteeinCharge2009icDeannaNeedell,2009.Allrightsreserved.Idedicatethisdissertationtoallmyloved

3、ones,thosewithmetodayandthosewhohavepassedon.iiContents1Introduction11.1Overview..................................11.1.1MainIdea.............................11.1.2ProblemFormulation.......................31.2Applications................................61.2.1E

4、rrorCorrection.........................61.2.2Imaging..............................71.2.3Radar...............................92MajorAlgorithmicApproaches102.1BasisPursuit...............................102.1.1Description............................112.1.2Restri

5、ctedIsometryCondition..................122.1.3MainTheorems..........................152.1.4NumericalResults........................182.1.5LinearProgramming.......................192.1.6Summary.............................222.2GreedyMethods....................

6、.........23iii2.2.1OrthogonalMatchingPursuit..................232.2.2StagewiseOrthogonalMatchingPursuit............272.2.3CombinatorialMethods.....................323Contributions363.1RegularizedOrthogonalMatchingPursuit...............363.1.1Description......

7、......................363.1.2MainTheorems..........................393.1.3ProofsofTheorems........................433.1.4ImplementationandRuntime..................633.1.5NumericalResults........................643.1.6Summary.............................683.2C

8、ompressiveSamplingMatchingPursuit................703.2.1Description............................713.2.2MainTheorem..........................743.2.3ProofsofTheorems........................7