Phd-Dual Methods for Total Variation-Based Image Restoration

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1、UniversityofCaliforniaLosAngelesDualMethodsforTotalVariation-BasedImageRestorationAdissertationsubmittedinpartialsatisfactionoftherequirementsforthedegreeDoctorofPhilosophyinMathematicsbyJamylleLauriceCarter2001cCopyrightbyJamylleLauriceCarter2001ThedissertationofJamylleLauriceCarter

2、isapproved.LievenVandenbergheStanleyJ.OsherMingGuTonyF.Chan,CommitteeChairUniversityofCalifornia,LosAngeles2001iiTomyparentsfortheirencouragementandtoGodforItsunconditionalloveandsupport.iiiTableofContents1Introduction................................11.1IntroductiontoResearchProblem..

3、................21.2SolvingPrimalTVProblem.....................31.3Effectsofβ..............................41.4DualTVProblem...........................41.4.1StatementofProblem....................41.4.2DerivationofProblem....................51.4.3ExplanationofProblem...................6

4、1.5StatementofPurpose.........................61.6AlgorithmforComparison......................72Primal-DualInteriorPointMethod.................82.1Description..............................92.2Comparison..............................113Primal-DualRelaxationMethods..................143.

5、1PrimalRelaxation...........................153.2DualRelaxation............................213.2.11DDualRelaxation......................213.2.22DDualRelaxation......................233.3HybridRelaxationDescription....................363.3.11DHybridRelaxation....................37iv3.3

6、.22DHybridRelaxation....................414BarrierRelaxationMethod......................534.1Description..............................544.2Examples...............................605Conclusion.................................725.11D...................................735.22D............

7、.......................73References...................................75vListofFigures2.1Alargevalueofβsmearstheedges.TheMuletinterior-pointmethoddoesrequiremoreiterationstosolvetheNewtonequationthandoestheCGMmethod.However,theMuletmethoddoesnotneedβ...............................122.

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