[66]Aubert G Vess A a variational method in image recovery.pdf

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1、AVariationalMethodinImageRecoveryAuthor(s):GillesAubertandLuminitaVeseReviewedwork(s):Source:SIAMJournalonNumericalAnalysis,Vol.34,No.5(Oct.,1997),pp.1948-1979Publishedby:SocietyforIndustrialandAppliedMathematicsStableURL:http://www.jstor.org/stable/2952025.Accessed:03/03/20

2、1203:28YouruseoftheJSTORarchiveindicatesyouracceptanceoftheTerms&ConditionsofUse,availableat.http://www.jstor.org/page/info/about/policies/terms.jspJSTORisanot-for-profitservicethathelpsscholars,researchers,andstudentsdiscover,use,andbuilduponawiderangeofcontentinatrusteddig

3、italarchive.Weuseinformationtechnologyandtoolstoincreaseproductivityandfacilitatenewformsofscholarship.FormoreinformationaboutJSTOR,pleasecontactsupport@jstor.org.SocietyforIndustrialandAppliedMathematicsiscollaboratingwithJSTORtodigitize,preserveandextendaccesstoSIAMJournal

4、onNumericalAnalysis.http://www.jstor.orgSIAMJ.NUMER.ANAL.?1997SocietyforIndustrialandAppliedMathematicsVol.34,No.5,pp.1948-1979,October1997016AVARIATIONALMETHODINIMAGERECOVERY*GILLESAUBERTtANDLUMINITAVESEtAbstract.Thispaperisconcernedwithaclassicaldenoisinganddeblurringprobl

5、eminimagerecovery.Ourapproachisbasedonavariationalmethod.ByusingtheLegendre-Fencheltransform,weshowhowthenonquadraticcriteriontobeminimizedcanbesplitintoasequenceofhalf-quadraticproblemseasiertosolvenumerically.Firstweproveanexistenceanduniquenessresult,andthenwedescribethea

6、lgorithmforcomputingthesolutionandwegiveaproofofconvergence.Finally,wepresentsomeexperimentalresultsforsyntheticandrealimages.Keywords.imageprocessing,Legendre-Fencheltransform,partialdifferentialequations,cal-culusofvariationsAMSsubjectclassifications.35J,49J,65NPII.S003614

7、299529230X1.Introduction.Animportantprobleminimageanalysisisthereconstruc-tionofanoriginalimagefdescribingarealscenefromanobservedimagep.Thetransformation(ordegradation)connectingftopisingeneraltheresultoftwophe-nomena.Thefirstphenomenonisdeterministicandisrelatedtothemodeof

8、imageacquisition(forexample,thecomputationofintegralprojectionsintomography