一種改進的高斯頻率域壓縮感知稀疏反演方法(英AbstractompressivesensingandsparseinversionmethodshavegainedasignificantamountofattentioninrecentyearsduetotheircapabilitytoaccuratelyreconstructsignalsfrommeasurementswithsignificantlylessdatathanpreviouslypossibleInthispaper,amodifiedGaussianfrequencydomaincompressivesensingandsparseinversionmethodisproposedwhichleveragestheprovenstrengthsofthetraditionalmethodtoenhanceitsaccuracyandperformance.Simulationresultsdemonstratethattheproposedmethodcanachieveahighersignal-to-noiseratioandabetterreconstructionqualitythanitstraditionalcounterpartwhilealsoreducingthecomputationalcomplexityoftheinversionprocedure.CompressivesensingCSisanemergingfieldthathasgarneredsignificantinterestinrecentyearsbecauseitleveragesthesparsityofsignalstoreducethenumberofmeasurementsrequiredtoaccuratelyreconstructthesignalThishasmanyadvantagesovertraditionalsignalprocessingmethodsincludingfasterdataacquisitiontimes,reducedpowerconsumptionandlowerdatastoragerequirements.CShasbeensuccessfullyappliedtoawiderangeoffields,includingmedicalimaging,wirelesscommunications,andsurveillance.OneofthemostcommonlyusedmethodsincompressivesensingistheGaussianfrequencydomaincompressivesensingandsparseinversionGFDCS)method.Inthismethod,compressivemeasurementsareacquiredbymultiplyingtheoriginalsignalwitharandomlygeneratedsensingmatrix.ThemeasurementsarethentransformedintothefrequencydomainusingtheFouriertransform,andthesparsesignalisreconstructedusingasparsitypromotingalgorithm.centyearsresearchershavemadenumerousimprovementstotheGFDCSmethod,withthegoalofimprovingitsreconstructionaccuracyreducingitscomputationalcomplexity,andenhancingitsrobustnesstonoiseInthispaper,weproposeamodifiedGFD-CSmethodthatcombinesseveraltechniquestoachievetheseobjectives.Theproposedmethodbuildsuponthewell-establishedGFD-CSmethodwithseveralkeymodificationsThefirstmodificationistheuseofahierarchicalsparsitypromotingalgorithmwhichpromotessparsityatboththesignallevelandthetransformlevel.Thisisachievedbypplyingthehierarchicalthresholdingtechniquetothecoefficientscorrespondingtothehigherfrequencycomponentsofthetransformedsignal.Thesecondmodificationistheuseofanovelerrorfeedbackmechanismwhichreducestheimpactofmeasurementnoiseonthereconstructedsignal.Specifically,theproposedmethodutilizesaniterativealgorithmthatupdatesthemeasurementerrorbasedonthedifferencebetweenthereconstructedsignalandthemeasuredsignal.Thisfeedbackmechanismeffectivelyincreasesthesignal-to-noiseratioofthereconstructedsignal,improvingitsaccuracyandrobustnesstonoise.Thethirdmodificationistheuseofalow-rankapproximationmethodwhichreducesthecomputationalcomplexityoftheinversionalgorithmwhilemaintainingreconstructionaccuracyThisisachievedbydecomposingthesensingmatrixintoaproductoftwolowerdimensionalmatriceswhichcanbesubsequentlyinvertedusingamoreefficientalgorithm.nResultsToevaluatetheeffectivenessoftheproposedmethod,weconductedsimulationsusingsyntheticdatasets.Threedifferentsignaltypeswereconsideredasinusoidalsignal,apulsesignal,andanimagesignalTheresultsofthesimulationswerecomparedtothoseobtainedusingthetraditionalGFD-CSmethod.ThesimulationresultsdemonstratethattheproposedmethodoutperformsthetraditionalGFDCSmethodintermsofsignal-to-noiseratioandreconstructionqualitySpecifically,theproposedmethodachievesahighersignalto-noiseratioandlowermeansquarederrorforallthreetypesofsignalsconsidered.Furthermore,theproposedmethodachievestheseresultswithareducedcomputationalcomplexitycomparedtothetraditionalmethod.nTheresultsofoursimulationsdemonstratetheeffectivenessoftheproposedmethodinenhancingtheaccuracyandperformanceoftheGFD-CSmethod.Thecombinationofsparsitypromotion,errorfeedback,ndlowrankapproximationtechniquessignificantlyimprovesthesignal