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1、2011-01-25TheCompressiveSensingTheoryAndPracticeofOMPAlgorithmAnOverviewofCompressiveSensingFor1-DsignalX∈RN×1,mostly，theinformationisredundant.。Wecancompressitbyorthogonaltransformation.coding：makeorthogonalmatrixΨ,transformationy=Ψx,remainthemostimportantKcomponentsofyandthecor
2、respondingpositions.decoding：putKcomponentsbacktothecorrespondingpositions,letotherpositionsbezero,makeΨH，inversetransformationx*=ΨHy*.CodingSamplingTransformationSignalxyDecodingReceiveddatayInversetransformationReconstructedsignalx*AnOverviewofCompressiveSensingButtherearesomef
3、lawsofthismethod:1)ConsideringtheShannonsamplingtheorem，thesamplingintervalwillbeverynarrowtogainbettersignalresolution，whichwillmaketheoriginalsignalverylong,sotheprocessingoftransformationcostslotsoftime.2)ThepositionsofKcomponentsrequiredtoremainvarywhilethesignalchanges.There
4、fore,thisstrategyisself-adaptive,andweneedtoallocatemorespacetostorethesepositions.3)Pooranti-interference.OnceoneoftheKcomponentslostintransmission,theoutputwillbechangedgreatly.AnOverviewofCompressiveSensingIn2004,DonohoandCandesputforwardthetheoryofcompressivesensing.Thistheor
5、yindicatesthatwhenthesignalissparseorcompressible,thesignalcanbereconstructedaccuratelyorapproximatelybygatheringveryfewprojectivevaluesofthesignal.Themeasuredvalueisnotthesignalitself,buttheprojectivevaluefromhigherdimensiontolowerdimension.CodingSparsesignalxMeasurement,codingy
6、DecodingReceivedsignalyDecoding,reconstructionConstructedsignalx*AnOverviewofCompressiveSensingTheadvantagesofcompressivesensing:1)Non-adaptive,breakthroughthelimitationofShannonsamplingtheorem.2)StrongAnti-interferenceability,everycomponentofthemeasurementisimportant,orunimporta
7、nt.Itcanstillbereconstructedwhilesomecomponentsarelost.Theapplicationprospectofcompressivesensingisbroad:digitalcameraandaudioacquisitiondevicewithlowcost;astronomy(starsaresparse);network;military.AnOverviewofCompressiveSensingSupposex(n)isadigitalsignal,ifit’saK-sparse(hasKnon-
8、zerovalues)orcompressiblesignal,thenweca
