压缩感知与单像素成像

|CompressiveSensingofImages关晨孙晓雯李显业1.IntroductionDetectorSensingSignalComputerCompressingStorageSavingSignalDetectorSensingCompressingStorageSavingEmmanuelCandèsZhexuanTao2.PrincipleS(n*1)Ψ(n*n)X(n*1)ksparsenessΦ(m*n)Y(m*1)Y=ΦΨS=ΦXWheremsatisfiedtheequationm≥C*k*log(n/k)(Cisaconstant)Usually,Ψisaknownbasis,knowledgeofXisequivalenttoknowledgeofS.HowtosolveXfromthefunctionY=ΦX.Thatisaconvexoptimizationproblem𝑋=argmin𝑋1𝑆.𝑡.Φ𝑋=𝑌Thisequationhasaconvenientclosedformsolutiongivenby𝑋=(ΦΦ𝑇)−1Φ𝑇Y2.PrincipleGenerallycompressivesensingreliedontheassumptionthatthesolutiontothel1minimizationproblemprovidesthecorrectsolutionandiscomputationallyfeasible.Howeverworkhasbeendonetofindalternativealgorithmsthatarefasterorgivesuperiorreconstructionperformance.MatchingPursuit(MP)OrthogonalMatchingPursuit(OMP)StagewiseOrthogonalMatchingPursuit(StOMP)CompressiveSamplingMatchingPursuit(CoSaMP)Two-StepIterativeShrinkageThresholding(TwIST)2.PrincipleInitialimagesparsetransformFFTDCTDWT……SparseimageMeasurementmatrixcompressedimageMeasurementmatrixSparseimageInversetransformationReconstructionalgorithms3.SimulationInitialimageDWTSparseMeasurementReconstructionDCTReconstructionSparsecompressionratio30%(OMP)DWTDCTCC0.93270.8825PSNR23.295520.83954.ApplicationSinglepixelcamera(computationalghostimaging)Y=ΦX4.ApplicationSinglepixelcamera(Compressiveghostimaging)LaserExpanderSLMObjectBDComputerY=ΦΨS=ΦX4.ApplicationInitialimageReconstructionfilteringcompressionratio:7.93%PSNR：62.048dB4.Application4.ApplicationThanks