压缩感知课件.ppt

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1、压缩感知理论与应用智能信息处理研究所智能感知与图像理解教育部重点实验室2011年8月IntelligentPerceptionandImageUnderstandingKeyLabofMinistryofChina上次课内容回顾Lecture1：压缩感知概述为什么研究压缩感知压缩感知的涵义压缩感知的过程压缩感知的关键问题FromNyquisttoCSCompressionOriginal2500KB100%Compressed950KB38%Compressed392KB15%Compressed148KB6%“Canwenot

2、justdirectlymeasurethepartthatwillnotendupbeingthrownaway?”DonohoSparserepresentationofanimageviaamultiscalewavelettransform.(a)Originalimage.(b)Waveletrepresentation.Largecoefficientsarerepresentedbylightpixels,whilesmallcoefficientsarerepresentedbydarkpixels.Observeth

3、atmostofthewaveletcoefficientsareclosetozero.Sparseinwavelet-domainSparseapproximationofanaturalimage.(a)Originalimage.(b)Approximationofimageobtainedbykeepingonlythelargest10%ofthewaveletcoefficients.Sparseinwavelet-domainOurPoint-Of-ViewCompressedSensing(CS)mustbebase

4、donsparsityandcompressibility.Thesignalsmustbesparseintime-domainorinfrquency-domain.CompressedSensing“Canwenotjustdirectlymeasurethepartthatwillnotendupbeingthrownaway?”Donoho“sensing…asawayofextractinginformationaboutanobjectfromasmallnumberofrandomlyselectedobservati

5、ons”Candèset.al.NyquistrateSamplingAnalogAudioSignalCompression(e.g.MP3)High-rateLow-rateCompressedSensingConceptGoal:Identifythebucketwithfakecoins.Nyquist:WeighacoinfromeachbucketCompressionBucket#numbers1numberCompressedSensing:Bucket#1numberWeighalinearcombina

6、tionofcoinsfromallbucketsMathematicalToolsnon-zeroentriesatleastmeasurementsRecovery:brute-force,convexoptimization,greedyalgorithms,andmore…CStheoryCompressedsensing(2003/4andon)–MainresultsMaximalcardinalityoflinearlyindependentcolumnsubsetsHardtocompute!isuniquely

7、determinedbyDonohoandElad,2003Smallestnumberofcolumnsthatarelinearly-dependent.isuniquelydeterminedbyisrandomwithhighprobabilityDonoho,2006andCandèset.al.,2006NP-hardConvexandtractableGreedyalgorithms:OMP,FOCUSS,etc.Donoho,2006andCandèset.al.,2006Tropp,Cotteret.al.Chene

8、t.al.andmanyotherCompressedsensing(2003/4andon)–MainresultsCStheoryDonohoandElad,2003RIPcriterion(a)Themeasure