(Burger)Inverse Problems

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1、LectureNotesInverseProblemsWinter2007/08MartinBurgerInstitutf¨urNumerischeundAngewandteMathematikWestf¨alischeWilhelms-Universit¨atM¨unstermartin.burger@uni-muenster.de1Contents1Introduction42ExamplesofInverseProblems62.1DifferentiationofData...............................62.2ComputerizedTomo

2、graphy:RadonInversion..................92.3ImageDenoisingandDeblurring.........................102.4ParameterIdentification..............................112.5ImpedanceTomography..............................132.6InverseScattering..................................143RegularizationofLinearIll-P

3、osedProblems163.1Ill-ConditionedMatrixEquations.........................163.2GeneralizedInverses................................193.3CompactLinearOperators............................213.4RegularizationMethods..............................243.5ConstructionofRegularizationMethods.............

4、........273.6ConvergenceRates.................................324Tikhonov-typeRegularization354.1TikhonovRegularization..............................354.2ConstructionofTikhonov-typeRegularizationMethods............414.3Maximum-EntropyRegularization........................414.4TotalVariationR

5、egularization..........................425IterativeRegularization475.1LandweberIteration................................475.2ConjugateGradientMethods...........................515.3Newton-typeMethods...............................525.4IterativeMethodsasTime-DiscreteFlows....................5

6、36Discretization546.1RegularizationbyProjection...........................546.2DiscretizationofRegularizedProblems......................566.3NumericalSolutionofDiscretizedProblems...................5727ParameterIdentification597.1DerivativesandtheAdjointMethod.......................607.2Regul

7、arization...................................627.2.1IterativeRegularizationbytheLevenberg-MarquardtMethod.....657.3LargeScaleProblems...............................658ShapeReconstructionProblems678.1ShapeSensitivityAnalysis..........................