资源描述:
《Optimal Sensing Matrix for Compressed Sensing》由会员上传分享,免费在线阅读,更多相关内容在学术论文-天天文库。
1、OptimalSensingMatrixforCompressedSensingLifengYu,HuangBaiandXiaofangWanCollegeofInformationEngineeringZhejiangUniversityofTechnology310014Hangzhou,Zhejiang,P.R.ChinaEmail:ylfeng28@sina.comAbstract—ThispaperpresentsanovelframeworkoffastandrecoveringsexactlyprovidedthatthematrixΘobeysaefficie
2、ntcompressedsamplingbasedontherestrictedisometryconditionknownasRIPorarelatedconditionknownasMIP.property(RIP).Theproposedframeworkprovidesthreefea-TwokindsofmatricesareavailableforCS.tures.i)Itisuniversalwithavarietyofsparsesignals.ii)ThefirstfamilyofsensingmatricesconsistsofrandomTherecon
3、structionerrorscanbeminimized.iii)Ithasfastcomputation,thatis,itneedsfewiterations.AllcurrentlyexistingGaussian/Bernoullimatrices(ormoregenerally,sub-Gaussianmethodsdon’tsatisfythesedesiredfeatures.Experimentalresultsrandommatrices).Forexample,Gaussiantypicallyhavearepresentedtoverifytheva
4、lidityaswellastoillustratetheboundedk-restrictedisometryconstantsforkproportionaltopromisingpotentialoftheproposedframework.nasngrows.IndexTerms—compressedsensing;RIP;MIP;optimization;Thesecondfamilyisrandomrowsofanyortho-normaleigenvalue;mutualcoherencematrix,suchaspartialFourierorHadamar
5、dmatrices.However,partialFouriermatrixisonlyincoherentwithI.INTRODUCTIONsignalswhicharesparseinthetimedomain,severelyCompressedsensingalsoknownas"compressedsensing"narrowingitsscopeofapplications."compressivesampling"and"(CS)"[1],[2],[3],anovelsensing/samplingparadigmthatgoesagainstthecomm
6、onwisdomindataacquisition.ContrarytooldpracticeofdataII.THEBASICS:RIPANDMIPacquisitionandreconstructionbasedontheShannon-NyquistInthisSection,wedetailsthepropertiesthatRIPandMIP.samplingprinciple,thenewtheoryshowsitispossibletoDefinition1[4],[5]:Foreachintegerk=1,2,...,definethereconstructim
7、agesorsignalsofscientificinterestaccuratelyisometryconstantδk∈(0,1)ofam×nmatrixΘ,withmn,andevenexactlyfromanumberofsampleswhichisfarasthesmallestnumbersuchthat:smallerthanthedesiredresolutionoftheimage/signal.(1−δ)v2≤Θv2≤(1+δ)v2(4)Supposethatweobservekl2