压缩感知理论及OMP算法.ppt

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压缩感知理论及OMP算法.ppt

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2011-01-25TheCompressiveSensingTheoryAndPracticeofOMPAlgorithm

AnOverviewofCompressiveSensingFor1-DsignalX∈RN×1,mostly，theinformationisredundant.。Wecancompressitbyorthogonaltransformation.coding：makeorthogonalmatrixΨ,transformationy=Ψx,remainthemostimportantKcomponentsofyandthecorrespondingpositions.decoding：putKcomponentsbacktothecorrespondingpositions,letotherpositionsbezero,makeΨH，inversetransformationx*=ΨHy*.CodingSamplingTransformationSignalxyDecodingReceiveddatayInversetransformationReconstructedsignalx*

AnOverviewofCompressiveSensingButtherearesomeflawsofthismethod:1)ConsideringtheShannonsamplingtheorem，thesamplingintervalwillbeverynarrowtogainbettersignalresolution，whichwillmaketheoriginalsignalverylong,sotheprocessingoftransformationcostslotsoftime.2)ThepositionsofKcomponentsrequiredtoremainvarywhilethesignalchanges.Therefore,thisstrategyisself-adaptive,andweneedtoallocatemorespacetostorethesepositions.3)Pooranti-interference.OnceoneoftheKcomponentslostintransmission,theoutputwillbechangedgreatly.

AnOverviewofCompressiveSensingIn2004,DonohoandCandesputforwardthetheoryofcompressivesensing.Thistheoryindicatesthatwhenthesignalissparseorcompressible,thesignalcanbereconstructedaccuratelyorapproximatelybygatheringveryfewprojectivevaluesofthesignal.Themeasuredvalueisnotthesignalitself,buttheprojectivevaluefromhigherdimensiontolowerdimension.CodingSparsesignalxMeasurement,codingyDecodingReceivedsignalyDecoding,reconstructionConstructedsignalx*

Theadvantagesofcompressivesensing:StrongAnti-interferenceability,everycomponentofthemeasurementisimportant,orunimportant.Itcanstillbereconstructedwhilesomecomponentsarelost.Non-adaptive,breakthroughthelimitationofShannonsamplingtheorem.Theapplica