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成像中的變分法-167 版權信息
- ISBN：9787510058424
- 條形碼：9787510058424 ; 978-7-5100-5842-4
- 裝幀：一般膠版紙
- 冊數：暫無
- 重量：暫無
- 所屬分類：>>
成像中的變分法-167 本書特色
《成像中的變分法(英文)》由世界圖書出版公司北京公司出版。
成像中的變分法-167 內容簡介
Imagmg is an interdisciplinary research area with profound applications in many areas of science, engineering, technology, and medicine. The most primitrve form of imaging is visual in,spection, which has dominated the area before the technical and computer revolution era. Today, computer imaging covers various aspects of data tiltering, pattern recognition, feature extraction., co'mputer aided mspection, and medical diagnosis. The above mentioned areas are treated in different scientific communities such as Imagin,g, In,verse Problems, Computer Vision, Signal and Image Processing,…, but all share the common thread of recovery of an object or one of its properties.
成像中的變分法-167 目錄
Part I Fundamentals of Imagmg
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 Thermoacoustic Computerzed Tomography
1.6 Schlieren Tomography
2 Image and Noise Models
2.1 Basic Concepts of Statistics
2.2 Digitzed (Discrete) Images
2.3 Noise Models
2.4 Priors for Images
2.5 Maximum A Posteriori Estimation
2.6 MAP Rstimation for Noisy Images
Part I Fundamentals of Imagmg
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 Thermoacoustic Computerzed Tomography
1.6 Schlieren Tomography
2 Image and Noise Models
2.1 Basic Concepts of Statistics
2.2 Digitzed (Discrete) Images
2.3 Noise Models
2.4 Priors for Images
2.5 Maximum A Posteriori Estimation
2.6 MAP Rstimation for Noisy Images
Part II Regularization
3 Variational R,egularzation Methods for the Solution of Inverse Problems
3.1 Quadratic Tikhonov R;egularization in Hilbert Spaces
3.2 Variational R,egularization Methods in Banach Spaces
3.3 Regularization with Sparsity Constraints
3.4 Linear Inverse Problems with Convex Constraints
3.5 Schlieren Tomography.
3.6 Further 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 R,egularization
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 Serru-group Theory and Scale Spaces
6.1 Linear Semi-group Theory
6.2 Non-linear Semi-groups in Hilbert Spaces
6.3 Non-Iinear Semi-groups in Banach Spaces
6.4 Axiomatic Approach to Scale Spaces
6.5 Evolution by Non-convex Energy Functionals
6.6 Enhancing
7 Inverse Scale Spaces
7.1 Iterative Tikhonov Regularization
7.2 Iterative Regularization with Bregman Distances
7.3Recent 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 Differentiable 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
10 Convex Analysis and Calculus of Variations
References
Nomenclature
Index
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 Thermoacoustic Computerzed Tomography
1.6 Schlieren Tomography
2 Image and Noise Models
2.1 Basic Concepts of Statistics
2.2 Digitzed (Discrete) Images
2.3 Noise Models
2.4 Priors for Images
2.5 Maximum A Posteriori Estimation
2.6 MAP Rstimation for Noisy Images
Part I Fundamentals of Imagmg
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 Thermoacoustic Computerzed Tomography
1.6 Schlieren Tomography
2 Image and Noise Models
2.1 Basic Concepts of Statistics
2.2 Digitzed (Discrete) Images
2.3 Noise Models
2.4 Priors for Images
2.5 Maximum A Posteriori Estimation
2.6 MAP Rstimation for Noisy Images
Part II Regularization
3 Variational R,egularzation Methods for the Solution of Inverse Problems
3.1 Quadratic Tikhonov R;egularization in Hilbert Spaces
3.2 Variational R,egularization Methods in Banach Spaces
3.3 Regularization with Sparsity Constraints
3.4 Linear Inverse Problems with Convex Constraints
3.5 Schlieren Tomography.
3.6 Further 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 R,egularization
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 Serru-group Theory and Scale Spaces
6.1 Linear Semi-group Theory
6.2 Non-linear Semi-groups in Hilbert Spaces
6.3 Non-Iinear Semi-groups in Banach Spaces
6.4 Axiomatic Approach to Scale Spaces
6.5 Evolution by Non-convex Energy Functionals
6.6 Enhancing
7 Inverse Scale Spaces
7.1 Iterative Tikhonov Regularization
7.2 Iterative Regularization with Bregman Distances
7.3Recent 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 Differentiable 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
10 Convex Analysis and Calculus of Variations
References
Nomenclature
Index
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成像中的變分法-167 節選
《成像中的變分法(英文)》由世界圖書出版公司北京公司出版。
成像中的變分法-167 作者簡介
Otmar Scherzer，Markus Grasmair， Harald Grossauer，Markus Haltmeier， Frank Lenzen是國際知名學者，在數學和物理學界享有盛譽。本書凝聚了作者多年科研和教學成果，適用于科研工作者、高校教師和研究生。
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