2D sparse signal recovery via 2D orthogonal matching pursuit .pdf

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1、SCIENCECHINAInformationSciences.RESEARCHPAPER.April2012Vol.55No.4:889–897doi:10.1007/s11432-012-4551-52Dsparsesignalrecoveryvia2DorthogonalmatchingpursuitFANGYong1∗,WUJiaJi2&HUANGBorMin31CollegeofInformationEngineering,NorthwestA&FUniversity,Yangling712100,China;2KeyLabora

2、toryofIntelligentPerceptionandImageUnderstandingofMinistryofEducationofChina,XidianUniversity,Xi’an710071,China;3SpaceScienceandEngineeringCenter,UniversityofWisconsin-Madison,Madison,WI53706,USAReceivedJune10,2011;acceptedOctober4,2011AbstractRecoveryalgorithmsplayakeyrol

3、eincompressivesampling(CS).MostofcurrentCSrecoveryalgo-rithmsareoriginallydesignedforone-dimensional(1D)signal,whilemanypracticalsignalsaretwo-dimensional(2D).Byutilizing2Dseparablesampling,2Dsignalrecoveryproblemcanbeconvertedinto1Dsignalrecoveryproblemsothatordinary1Drec

4、overyalgorithms,e.g.orthogonalmatchingpursuit(OMP),canbeapplieddirectly.However,evenwith2Dseparablesampling,thememoryusageandcomplexityatthedecoderarestillhigh.Thispaperdevelopsanovelrecoveryalgorithmcalled2D-OMP,whichisanextensionof1D-OMP.Inthe2D-OMP,eachatominthedictiona

5、ryisamatrix.Ateachiteration,thedecoderprojectsthesamplematrixonto2Datomstoselectthebestmatchedatom,andthenrenewstheweightsforallthealreadyselectedatomsviatheleastsquares.Weshowthat2D-OMPisinfactequivalentto1D-OMP,butitreducesrecoverycomplexityandmemoryusagesignificantly.Wha

6、t’smoreimportant,byutilizingthesamemethodologyusedinthispaper,onecanevenobtainhigherdimensionalOMP(say3D-OMP,etc.)withease.Keywordscompressivesampling,2Dsparsesignal,recoveryalgorithm,orthogonalmatchingpursuitCitationFangY,WuJJ,HuangBM.2Dsparsesignalrecoveryvia2Dorthogonal

7、matchingpursuit.SciChinaInfSci,2012,55:889–897,doi:10.1007/s11432-012-4551-51IntroductionLetx∈Rnbeaone-dimensional(1D)signalandΨ∈Rn×nanorthonormaltransformmatrix,whereRisthesetofrealnumbers.Ifx=Ψzandthereareonlyknspikes(nonzeroentries)inz,wesaythatxisk-sparseinΨdomain.Wes

8、amplexbyΦ∈Rm×n(k