Variational methods in imaging
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ISBN：9787510058424
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简介
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.
目录
Part I Fundamentals of Imagmg1 Case Examples of Imaging1.1 Denoising1.2 Chopping and Nodding1.3 Image Inpainting 1.4 X-ray-Based Computerized Tomography1.5 Thermoacoustic Computerzed Tomography1.6 Schlieren Tomography2 Image and Noise Models 2.1 Basic Concepts of Statistics2.2 Digitzed （Discrete） Images2.3 Noise Models2.4 Priors for Images2.5 Maximum A Posteriori Estimation2.6 MAP Rstimation for Noisy Images Part II Regularization3 Variational R,egularzation Methods for the Solution of Inverse
Problems3.1 Quadratic Tikhonov R;egularization in Hilbert Spaces3.2 Variational R,egularization Methods in Banach Spaces3.3 Regularization with Sparsity Constraints3.4 Linear Inverse Problems with Convex Constraints3.5 Schlieren Tomography.3.6 Further Literature on Regularization Methods for Inverse
Problems 4 Convex Regularization Methods for Denoising4.1 The Number4.2 Characterization of Minimizers4.3 One-dimensional Results4.4 Taut String Algorithm4.5 Mumford-Shah Regularization4.6 Recent Topics on Denoising with Variational Methods5 Variational Calculus for Non-convex R,egularization5.1 Direct Methods 5.2 Relaxation on Sobolev Spaces5.3 Relaxation on BV5.4 Applications in Non-convex Regularization5.5 One-dimensional Results5.6 Examples6 Serru-group Theory and Scale Spaces6.1 Linear Semi-group Theory6.2 Non-linear Semi-groups in Hilbert Spaces6.3 Non-Iinear Semi-groups in Banach Spaces6.4 Axiomatic Approach to Scale Spaces6.5 Evolution by Non-convex Energy Functionals6.6 Enhancing7 Inverse Scale Spaces7.1 Iterative Tikhonov Regularization7.2 Iterative Regularization with Bregman Distances7.3Recent Topics on Evolutionary Equations for Inverse
Problems Part III Mathematical Foundations8 Functional Analysis8.1 General Topology8.2 Locally Convex Spaces8.3 Bounded Linear Operators and Functionals8.4 Linear Operators in Hilbert Spaces8.5 Weak and Weak Topologies8.6 Spaces of Differentiable Functions9 Weakly Differentiable Functions9.1 Measure and Integration Theory9.2 Distributions and Distributional Derivatives9.3 Geometrical Properties of Functions and Domains9.4 Sobolev Spaces10 Convex Analysis and Calculus of VariationsReferencesNomenclatureIndex 显示全部信息
Problems3.1 Quadratic Tikhonov R;egularization in Hilbert Spaces3.2 Variational R,egularization Methods in Banach Spaces3.3 Regularization with Sparsity Constraints3.4 Linear Inverse Problems with Convex Constraints3.5 Schlieren Tomography.3.6 Further Literature on Regularization Methods for Inverse
Problems 4 Convex Regularization Methods for Denoising4.1 The Number4.2 Characterization of Minimizers4.3 One-dimensional Results4.4 Taut String Algorithm4.5 Mumford-Shah Regularization4.6 Recent Topics on Denoising with Variational Methods5 Variational Calculus for Non-convex R,egularization5.1 Direct Methods 5.2 Relaxation on Sobolev Spaces5.3 Relaxation on BV5.4 Applications in Non-convex Regularization5.5 One-dimensional Results5.6 Examples6 Serru-group Theory and Scale Spaces6.1 Linear Semi-group Theory6.2 Non-linear Semi-groups in Hilbert Spaces6.3 Non-Iinear Semi-groups in Banach Spaces6.4 Axiomatic Approach to Scale Spaces6.5 Evolution by Non-convex Energy Functionals6.6 Enhancing7 Inverse Scale Spaces7.1 Iterative Tikhonov Regularization7.2 Iterative Regularization with Bregman Distances7.3Recent Topics on Evolutionary Equations for Inverse
Problems Part III Mathematical Foundations8 Functional Analysis8.1 General Topology8.2 Locally Convex Spaces8.3 Bounded Linear Operators and Functionals8.4 Linear Operators in Hilbert Spaces8.5 Weak and Weak Topologies8.6 Spaces of Differentiable Functions9 Weakly Differentiable Functions9.1 Measure and Integration Theory9.2 Distributions and Distributional Derivatives9.3 Geometrical Properties of Functions and Domains9.4 Sobolev Spaces10 Convex Analysis and Calculus of VariationsReferencesNomenclatureIndex 显示全部信息
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