成像中的变分法
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广东广州
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作者(奥)斯科泽
出版社世界图书出版公司
ISBN9787510058424
出版时间2013-03
装帧其他
开本其他
定价59元
货号2604926
上书时间2023-09-03
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目录
Part I Fundamentals Of Imaging
1 Case Examples Of Imaging
1.1 Denoising
1.2 Chopping And Nodding
1.3 Image Inpainting
1.4 X-Ray-Based Computerized Tomography
1.5 Thermoaconstic Computerized Tomography
1.6 Schlieren Tomography
2 Image And Noise Models
2.1 Basic Concepts Of Statistics
2.2 Digitized (Discrete) Images
2.3 Noise Models
2.4 Priors For Images
2.5 Maximum A Posteriori Estimation
2.6 Map Estimation For Noisy Images
Part Ii Regularization
Variational Regularization Methods For The Solution Of Inverse Problems
3.1 Quadratic Tikhonov Regularization In Hilbert Spaces
3.2 Variational Regularization Methods In Banach Spaces
3.3 Regularization With Sparsity Constraints
3.4 Linear Inverse Problems With Convex Constraints
3.5 Schlieren Tomography
3.6 Fulrther Literature On Regularization Methods For Inverse Problems
4 Convex Regularization Methods For Denoising
4.1 The *-Number
4.2 Characterization Of Minimizers
4.3 One-Dimensional Results
4.4 Taut String Algorithm
4.5 Mumford-Shah Regularization
4.6 Recent Topics On Denoising With Variational Methods
5 Variational Calculus For Non-Convex Regularization
5.1 Direct Methods
5.2 Relaxation On Sobolev Spaces
5.3 Relaxation On Bv
5.4 Applications In Non-Convex Regularization
5.5 One-Dimensional Results
5.6 Examples
6 Semi-Group Theory And Scale Spaces
6.1 Linear Semi-Group Theory
6.2 Non-Linear Semi-Groups In Hilbert Spaces
6.3 Non-Linear Semi-Groups In Banach Spaces
6.4 Axiomatic Approach To Scale Spaces
6.5 Evolution By Non-Convex Energy Functionals
6.6 Enhancing
Inverse Scale Spaces
7.1 Iterative Tikhonov Regularization
7.2 Iterative Regularization With Bregm/M Distances
7.3 Recent Topics On Evolutionary Equations For Inverse Problems
Part Iii Mathematical Foundations
8 Functional Analysis
8.1 General Topology
8.2 Locally Convex Spaces
8.3 Bounded Linear Operators And Functionals
8.4 Linear Operators In Hilbert Spaces
8.5 Weak And Weak* Topologies
8.6 Spaces Of Differentiable Functions
9 Weakly Different/Able Functions
9.1 Measure And Integration Theory
9.2 Distributions And Distributional Derivatives
9.3 Geometrical Properties Of Functions And Domains
9.4 Sobolev Spaces
9.5 Convolution
9.6 Sobolev Spaces Of Fractional Order
9.7 Bochner Spaces
9.8 Functions Of Bounded Variation
10 Convex Analysis And Calculus Of Variations
10.1 Convex And Lower Semi-Continuous Functionals
10.2 Fenchel Duality And Subdifferentiability
10.3 Duality Mappings
10.4 Differentiability Of Functionals And Operators
10.5 Derivatives Of Integral Functionals On Lp(Ω)
References
Nomenclature
Index
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