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1、ThePhysicsofCompressiveSensingandtheGradient-BasedRecoveryAlgorithmsQiDaiandWeiShaDepartmentofElectricalandElectronicEngineering,TheUniversityofHongKong,HongKong,China.Email:daiqi@hku.hk(QiDai);wsha@eee.hku.hk(WeiSha)ResearchReportCompiledJune8,2009Thephysicsofcompressivesensing(CS)andthegrad
2、ient-basedrecoveryalgorithmsarepresented.First,thedifferentformsforCSaresummarized.Second,thephysicalmeaningsofcoherenceandmeasurementaregiven.Third,thegradient-basedrecoveryalgorithmsandtheirgeometryexplanationsareprovided.Finally,weconcludethereportandgivesomesuggestionforfuturework.Keywords
3、:CompressiveSensing;Coherence;Measurement;Gradient-BasedRecoveryAlgorithms.c2009OpticalSocietyofAmerica1.Introduction(d)Iffissparseinthetransform-domainandthemeasurementsareacquiredinthetransform-domainThewell-knownNyquist/Shannonsamplingtheoremalso,thentheoptimizationproblemcanbegivenbythatt
4、hesamplingratemustbeatleasttwicethemax-imumfrequencyofthesignalisagoldenruleusedinminkf˜k1s.t.M0f˜=˜y.(4)visualandaudioelectronics,medicalimagingdevices,ra-dioreceiversandsoon.However,canwesimplyrecoveraFromtheaboveequations,themeaningsofthespar-signalfromasmallnumberoflinearmeasurements?Yes,
5、sitycanbegeneralized.Ifthenumberofthenon-zeroele-wecan,answeredfirmlybyEmmanuelJ.Cand`es,Justinmentsisverysmallcomparedwiththelengthofthetime-Romberg,andTerenceTao[1][2][3].Theybroughtusdomainsignal,thesignalissparseinthetime-domain.thetoolcalledCompressiveSensing(CS)[4][5][6]sev-Ifthemostimpo
6、rtantKcomponentsinthetransform-eralyearsagowhichavoidslargedigitaldatasetanddomaincanrepresentsignalaccurately,wecansaytheenablesustobuildthedatacompressiondirectlyfromsignalissparseinthetransform-domain.Becausewecantheacquisition.ThemathematicaltheoryunderlyingCSsetotherunimportantcomponents
7、tobezeroandimple-isdeepandbeautifulanddrawsfromdiversefields,butmenttheinversetransform,thetime-domainsignalcanwedon’tfocustoomuchonthemathematicalproofs.bereconstructedwithverysmallnumericalerror.TheHere,wewillgivesomephysicalexplanationsandd
