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1、2664IEEETRANSACTIONSONSIGNALPROCESSING,VOL.42,NO.10,OCTOBER1994Space-AlternatingGeneralizedExpectation-MaximizationAlgorithmJeffreyA.Fessler,Member,IEEE,andAlfred0.Hero,Member,IEEEAbstract-Theexpectation-maximization(EM)methodcannecessitatesoverlyinformativecomplete-dataspace
2、s,whichinfacilitatemaximizinglikelihoodfunctionsthatariseinstatis-turnleadtoslowconvergence.Inthispaperweshowimprovedticalestimationproblems.IntheclassicalEMparadigm,oneconvergenceratesbyupdatingtheparameterssequentiallyiniterativelymaximizestheconditionallog-likelihoodofasin
3、gleunobservablecompletedataspace,ratherthanmaximizingthesmallgroups.intractablelikelihoodfunctionforthemeasuredorincompleteTheconvergencerateofanEMalgorithmisinverselydata.EMalgorithmsupdateallparameterssimultaneously,whichrelatedtotheFisherinformationofitscomplete-dataspace[
4、13,hastwodrawbacks:1)slowconvergence,and2)difficultmaxi-andwehavepreviouslyshownthatless-informativecomplete-mizationstepsduetocouplingwhensmoothnesspenaltiesaredataspacesleadtoimprovedasymptoticconvergenceratesused.Thispaperdescribesthespace-alternatinggeneralizedEM[4]-[6].L
5、essinformativecomplete-dataspacescanalsolead(SAGE)method,whichupdatestheparameterssequentiallybytolargerstepsizesandgreaterlikelihoodincreasesintheearlyalternatingbetweenseveralsmallhidden-dataspacesdefinedbyiterations[5]-[7].Sincetherelationshipbetweencomplete-datathealgorit
6、hmdesigner.Weprovethatthesequenceofestimatesspaceinformationandconvergenceisthereforemorethanmonotonicallyincreasesthepenalized-likelihoodobjective,wede-justanasymptoticphenomenon,webelievethatoneshouldriveasymptoticconvergencerates,andweprovidesufficientcon-ditionsformonoton
7、econvergenceinnorm.Twosignalprocessingstrivetominimizetheinformationofthecomplete-dataspace.applicationsillustratethemethod:estimationofsuperimposedHowever,intheclassicalEMformulationalessinformativesignalsinGaussiannoise,andimagereconstructionfromPoissoncompletedataspacecanl
8、eadtoanintractablemaximizationmeasurements.Inbothapplications,ourSAG
