数学经典教材：成像中的变分法（影印版）（英文版）

图书标准信息

• 作者 [奥]斯科泽（Scherzer O.） 著
• 出版社 世界图书出版公司
• 出版时间 2013-03
• 版次 1
• ISBN 9787510058424
• 定价 59.00元
• 装帧 平装
• 开本 24开
• 纸张 胶版纸
• 页数 320页
• 正文语种 英语

【内容简介】

　　Imagmgisaninterdisciplinaryresearchareawithprofoundapplicationsinmanyareasofscience，engineering，technology，andmedicine.Themostprimitrveformofimagingisvisualin，spection，whichhasdominatedtheareabeforethetechnicalandcomputerrevolutionera.Today，computerimagingcoversvariousaspectsofdatatiltering，patternrecognition，featureextraction.，co'mputeraidedmspection，andmedicaldiagnosis.TheabovementionedareasaretreatedindifferentscientificcommunitiessuchasImagin，g，In，verseProblems，ComputerVision，SignalandImageProcessing，…，butallsharethecommonthreadofrecoveryofanobjectoroneofitsproperties.

【作者简介】

Otmar Scherzer，Markus Grasmair， Harald Grossauer，Markus Haltmeier， Frank Lenzen是国际知名学者，在数学和物理学界享有盛誉。本书凝聚了作者多年科研和教学成果，适用于科研工作者、高校教师和研究生。

【目录】

PartIFundamentalsofImagmg
1CaseExamplesofImaging
1.1Denoising
1.2ChoppingandNodding
1.3ImageInpainting
1.4X-ray-BasedComputerizedTomography
1.5ThermoacousticComputerzedTomography
1.6SchlierenTomography
2ImageandNoiseModels
2.1BasicConceptsofStatistics
2.2Digitzed（Discrete）Images
2.3NoiseModels
2.4PriorsforImages
2.5MaximumAPosterioriEstimation
2.6MAPRstimationforNoisyImages

PartIIRegularization
3VariationalR,egularzationMethodsfortheSolutionofInverseProblems
3.1QuadraticTikhonovR;egularizationinHilbertSpaces
3.2VariationalR,egularizationMethodsinBanachSpaces
3.3RegularizationwithSparsityConstraints
3.4LinearInverseProblemswithConvexConstraints
3.5SchlierenTomography.
3.6FurtherLiteratureonRegularizationMethodsforInverseProblems
4ConvexRegularizationMethodsforDenoising
4.1TheNumber
4.2CharacterizationofMinimizers
4.3One-dimensionalResults
4.4TautStringAlgorithm
4.5Mumford-ShahRegularization
4.6RecentTopicsonDenoisingwithVariationalMethods
5VariationalCalculusforNon-convexR,egularization
5.1DirectMethods
5.2RelaxationonSobolevSpaces
5.3RelaxationonBV
5.4ApplicationsinNon-convexRegularization
5.5One-dimensionalResults
5.6Examples
6Serru-groupTheoryandScaleSpaces
6.1LinearSemi-groupTheory
6.2Non-linearSemi-groupsinHilbertSpaces
6.3Non-IinearSemi-groupsinBanachSpaces
6.4AxiomaticApproachtoScaleSpaces
6.5EvolutionbyNon-convexEnergyFunctionals
6.6Enhancing
7InverseScaleSpaces
7.1IterativeTikhonovRegularization
7.2IterativeRegularizationwithBregmanDistances
7.3RecentTopicsonEvolutionaryEquationsforInverseProblems

PartIIIMathematicalFoundations
8FunctionalAnalysis
8.1GeneralTopology
8.2LocallyConvexSpaces
8.3BoundedLinearOperatorsandFunctionals
8.4LinearOperatorsinHilbertSpaces
8.5WeakandWeakTopologies
8.6SpacesofDifferentiableFunctions
9WeaklyDifferentiableFunctions
9.1MeasureandIntegrationTheory
9.2DistributionsandDistributionalDerivatives
9.3GeometricalPropertiesofFunctionsandDomains
9.4SobolevSpaces
10ConvexAnalysisandCalculusofVariations
References
Nomenclature
Index