一种改进的高斯频率域压缩感知稀疏反演方法（英文）

一种改进的高斯频率域压缩感知稀疏反演方法英文AbstractCompressive sensingand sparseinversion methodshave gainedasignificant amountof attentionin recent years dueto theircapability toaccuratelyreconstruct signalsfrom measurementswith significantlyless datathanpreviously possible.In thispaper,a modifiedGaussian frequencydomaincompressive sensingand sparseinversion methodis proposed,which leverages the provenstrengths of the traditionalmethod toenhanceits accuracy and performance.Simulation results demonstrate that theproposed methodcan achievea highersignal-to-noise ratioand abetterreconstruction qualitythan itstraditional counterpart,while alsoreducing thecomputational complexity of the inversion procedure.IntroductionCompressive sensingCS isan emergingfield thathas garneredsignificantinterest inrecentyearsbecause itleveragesthesparsity of signalsto reducethe numberof measurementsrequired to accurately reconstructthe signal.This hasmany advantagesover traditionalsignal processingmethods,including fasterdata acquisitiontimes,reduced powerconsumption,and lowerdata storagerequirements.CS hasbeen successfullyappliedtoa wide range of fields,including medicalimaging,wirelesscommunications,and surveillance.One ofthe mostcommonly usedmethods incompressive sensingis theGaussianfrequency domaincompressive sensingand sparseinversionGFD-CS method.In thismethod,compressive measurementsare acquiredbymultiplying theoriginal signalwith arandomly generatedsensing matrix.The measurementsare thentransformed into the frequencydomain usingtheFourier transform,and thesparse signalis reconstructedusing asparsitypromoting algorithm.In recentyears,researchers havemade numerousimprovements totheGFD-CS method,with thegoal ofimproving itsreconstruction accuracy,reducing itscomputational complexity,and enhancingits robustnessto noise.In thispaper,we proposea modifiedGFD-CS methodthat combinesseveraltechniques toachieve theseobjectives.Proposed MethodTheproposed methodbuilds upon the well-established GFD-CS method,with severalkey modifications.The firstmodification isthe useof ahierarchicalsparsity-promoting algorithm,which promotessparsity atboththe signallevel and the transformlevel.This isachieved byapplying thehierarchicalthresholding techniquetothecoefficients correspondingto thehigherfrequency componentsofthetransformed signal.The secondmodification isthe useof anovel error feedback mechanism,which reducesthe impactof measurementnoise onthe reconstructed signal.Specifically,the proposedmethod utilizesan iterativealgorithm thatupdatesthe measurementerror basedonthedifference betweenthe reconstructedsignalandthemeasured signal.This feedbackmechanism effectivelyincreasesthesignal-to-noise ratioofthereconstructedsignal,improving itsaccuracyand robustnessto noise.The thirdmodification isthe useof alow-rank approximationmethod,which reducesthe computationalcomplexity ofthe inversionalgorithm whilemaintainingreconstruction accuracy.This isachieved bydecomposing thesensingmatrix intoa productof twolower dimensionalmatrices,which canbesubsequently invertedusing amore efficientalgorithm.Simulation ResultsToevaluate the effectiveness ofthe proposedmethod,we conductedsimulationsusing syntheticdata sets.Three differentsignal typeswereconsidered:a sinusoidalsignal,a pulsesignal,and animage signal.Theresults ofthe simulationswere compared to thoseobtained usingthetraditional GFD-CS method.The simulationresultsdemonstratethatthe proposed methodoutperformsthe traditionalGFD-CS method in termsofsignal-to-noise ratioandreconstruction quality.Specifically,the proposedmethod achievesahigher signal-to-noise ratioand lowermean squarederror forall threetypesof signalsconsidered.Furthermore,theproposedmethod achievestheseresults witha reducedcomputationalcomplexitycomparedtothe traditionalmethod.ConclusionThe resultsof oursimulations demonstratetheeffectivenessof theproposedmethodinenhancing theaccuracyandperformance ofthe GFD-CSmethod.The combinationof sparsitypromotion,errorfeedback,andlow-rank approximationtechniques significantlyimproves thesignal-to-noiseratio andreconstruction quality,while reducingthe computationalcomplexityof theinversionprocedure.Our proposedmethod haspotential applicationsinawiderangeoffields,including medicalimaging,wireless communications,and surveillance.。