Cramér-Rao Bound for Circular Complex Independent Component Analysis - Springer

10
1/29/2015 CramérRao Bound for Circular Complex Independent Component Analysis Springer http://link.springer.com/chapter/10.1007/9783642285516_6#page2 1/10 Look Inside Get Access Find out how to access previewonly content Latent Variable Analysis and Signal Separation Lecture Notes in Computer Science Volume 7191, 2012, pp 4249 CramérRao Bound for Circular Complex Independent Component Analysis Abstract Despite an increased interest in complex independent component analysis (ICA) during the last two decades, a closedform expression for the Cramér Rao bound (CRB) of the complex ICA problem has not yet been established. In this paper, we fill this gap for the noiseless case and circular sources. The CRB depends on the distributions of the sources only through two characteristic values which can be easily calculated. In addition, we study the CRB for the family of circular complex generalized Gaussian distributions (GGD) in more detail and compare it to simulation results using several ICA estimators. Page %P Page 1

description

Cramér-Rao Bound for Circular Complex Independent Component Analysis

Transcript of Cramér-Rao Bound for Circular Complex Independent Component Analysis - Springer

  • 1/29/2015 CramrRaoBoundforCircularComplexIndependentComponentAnalysisSpringer

    http://link.springer.com/chapter/10.1007/9783642285516_6#page2 1/10

    LookInsideGetAccessFindouthowtoaccesspreviewonlycontentLatentVariableAnalysisandSignalSeparationLectureNotesinComputerScienceVolume7191,2012,pp4249

    CramrRaoBoundforCircularComplexIndependentComponentAnalysisAbstractDespiteanincreasedinterestincomplexindependentcomponentanalysis(ICA)duringthelasttwodecades,aclosedformexpressionfortheCramrRaobound(CRB)ofthecomplexICAproblemhasnotyetbeenestablished.Inthispaper,wefillthisgapforthenoiselesscaseandcircularsources.TheCRBdependsonthedistributionsofthesourcesonlythroughtwocharacteristicvalueswhichcanbeeasilycalculated.Inaddition,westudytheCRBforthefamilyofcircularcomplexgeneralizedGaussiandistributions(GGD)inmoredetailandcompareittosimulationresultsusingseveralICAestimators.

    Page%P

    Page1

  • 1/29/2015 CramrRaoBoundforCircularComplexIndependentComponentAnalysisSpringer

    http://link.springer.com/chapter/10.1007/9783642285516_6#page2 2/10

  • 1/29/2015 CramrRaoBoundforCircularComplexIndependentComponentAnalysisSpringer

    http://link.springer.com/chapter/10.1007/9783642285516_6#page2 3/10

    NoBodyTexttranslateme!Page2

  • 1/29/2015 CramrRaoBoundforCircularComplexIndependentComponentAnalysisSpringer

    http://link.springer.com/chapter/10.1007/9783642285516_6#page2 4/10

  • 1/29/2015 CramrRaoBoundforCircularComplexIndependentComponentAnalysisSpringer

    http://link.springer.com/chapter/10.1007/9783642285516_6#page2 5/10

    NoBodyTexttranslateme!

    ChapterMetrics1Citation

  • 1/29/2015 CramrRaoBoundforCircularComplexIndependentComponentAnalysisSpringer

    http://link.springer.com/chapter/10.1007/9783642285516_6#page2 6/10

    RelatedContent

    References(14)

    1. Wirtinger,W.:ZurformalenTheoriederFunktionenvonmehrkomplexenVernderlichen.MathematischeAnnalen97(1),357375(1927)CrossRef

    2. Eriksson,J.,Koivunen,V.:ComplexrandomvectorsandICAmodels:identifiability,uniqueness,andseparability.IEEETransactionsonInformationTheory52(3),10171029(2006)CrossRef

    3. Tichavsky,P.,Koldovsky,Z.,Oja,E.:PerformanceanalysisoftheFastICAalgorithmandCramrRaoboundsforlinearindependentcomponentanalysis.IEEETrans.onSig.Proc.54(4)(April2006)

    4. Ollila,E.,Kim,H.J.,Koivunen,V.:CompactCramrRaoboundexpressionforindependentcomponentanalysis.IEEETrans.onSig.Proc.56(4)(April2008)

    5. DeLathauwer,L.,DeMoor,B.:Ontheblindseparationofnoncircularsources.In:EUSIPCO2002,Toulouse,France(September2002)

    6. Douglas,S.C.:Fixedpointalgorithmsfortheblindseparationofarbitrarycomplexvaluednongaussiansignalmixtures.EURASIPJ.Appl.SignalProcess.2007(1)(January2007)

    7. Li,H.,Adali,T.:AlgorithmsforcomplexMLICAandtheirstabilityanalysisusingWirtingercalculus.IEEETrans.onSig.Proc.58(12),61566167(2010)CrossRef

    8. Li,X.L.,Adali,T.:Complexindependentcomponentanalysisbyentropyboundminimization.IEEETransactionsonCircuitsandSystemsI:RegularPapers57(7),14171430(2010)CrossRef

    9. Novey,M.,Adali,T.:Adaptablenonlinearityforcomplexmaximizationofnongaussianityandafixedpointalgorithm.In:Proc.IEEEWorkshoponMachineLearningforSignalProcessing(September2006)

  • 1/29/2015 CramrRaoBoundforCircularComplexIndependentComponentAnalysisSpringer

    http://link.springer.com/chapter/10.1007/9783642285516_6#page2 7/10

    10. Remmert,R.:Theoryofcomplexfunctions.Graduatetextsinmathematics.Springer,Heidelberg(1991)

    11. Brandwood,D.H.:Acomplexgradientoperatoranditsapplicationinadaptivearraytheory.IEEProc.130,1116(1983)

    12. Ollila,E.,Koivunen,V.,Eriksson,J.:OntheCramrRaoboundfortheconstrainedandunconstrainedcomplexparameters.In:Proc.IEEESensorArrayandMultichannelSignalProcessingWorkshop,SAM(2008)

    13. Jagannatham,A.K.,Rao,B.D.:CramrRaolowerboundforconstrainedcomplexparameters.IEEESig.Proc.Letters11(11)(November2004)

    14. Novey,M.,Adali,T.,Roy,A.:Acomplexgeneralizedgaussiandistributioncharacterization,generation,andestimation.IEEETrans.onSig.Proc.58(3),14271433(2010)CrossRef

    AboutthisChapter

    TitleCramrRaoBoundforCircularComplexIndependentComponentAnalysis

    BookTitleLatentVariableAnalysisandSignalSeparation

    BookSubtitle10thInternationalConference,LVA/ICA2012,TelAviv,Israel,March1215,2012.Proceedings

    Pagespp4249

    Copyright2012

    DOI10.1007/9783642285516_6

    PrintISBN9783642285509

    OnlineISBN9783642285516

    SeriesTitleLectureNotesinComputerScience

    SeriesVolume

  • 1/29/2015 CramrRaoBoundforCircularComplexIndependentComponentAnalysisSpringer

    http://link.springer.com/chapter/10.1007/9783642285516_6#page2 8/10

    7191SeriesISSN

    03029743Publisher

    SpringerBerlinHeidelbergCopyrightHolder

    SpringerVerlagGmbHBerlinHeidelbergAdditionalLinks

    AboutthisBook

    Topics

    PatternRecognition

    ImageProcessingandComputerVision

    SimulationandModeling

    AlgorithmAnalysisandProblemComplexity

    DiscreteMathematicsinComputerScience

    SpecialPurposeandApplicationBasedSystems

    Keywords

    CramrRaobound

    FisherInformation

    independentcomponentanalysis

    blindsourceseparation

    circularcomplexdistribution

    IndustrySectors

  • 1/29/2015 CramrRaoBoundforCircularComplexIndependentComponentAnalysisSpringer

    http://link.springer.com/chapter/10.1007/9783642285516_6#page2 9/10

    Electronics

    Telecommunications

    IT&Software

    eBookPackages

    eBookPackageenglishComputerScience

    eBookPackageenglishfullCollection

    Editors

    FabianTheis

    AndrzejCichocki

    ArieYeredor

    MichaelZibulevsky

    Authors

    BenediktLoesch(16)

    BinYang(16)

    AuthorAffiliations

    16.InsituteforSignalProcessingandSystemTheory,UniversityofStuttgart,Germany

    Continuereading...ToviewtherestofthiscontentpleasefollowthedownloadPDFlinkabove.

    Over8.5millionscientificdocumentsatyourfingertips

  • 1/29/2015 CramrRaoBoundforCircularComplexIndependentComponentAnalysisSpringer

    http://link.springer.com/chapter/10.1007/9783642285516_6#page2 10/10

    SpringerInternationalPublishingAG,PartofSpringerScience+BusinessMedia