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成像中的變分法(簡體書)
人民幣定價:59元
定  價:NT$354元
優惠價: 5177
可得紅利積點:5 點

庫存:2

商品簡介

目次

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.本書致力於研究成像處理中的方法,本著數學的嚴謹,用逆問題的觀點研究這個科目。更重要的,本書從確定性、幾何和隨機的觀點研究變分法,架起了成像分析中規範理論和逆問題的橋樑,圖形分析中的案例來解釋變分法,如去噪、熱聲學、計算斷層照相法中的應用,討論了非凸變量微積分、形態學分析和水平集之間的聯繫。分析變分法包括變分法的經典分析、現代分析如G規範性質和非凸變量分析,運用數值例子提高學習這本書的研究生和應用數學的研究人員理論水平。本書可以作為成像處理及和逆過程課程的一本很好的研究生水平的教程,也可以是學習規範理論的補充教程。成像處理領域的計算機專家也會從這本書中受益。
目次:(一)成像基礎:成像案例;成像和噪音模型;(二)正規化:逆問題解的變分規範化方法;降噪中的凸規範化方法;非凸正規化的變量微積分;半群理論和尺度空間;逆尺度空間;(三)數學基礎:泛函分析;若微分函數;凸分析和變量微積分。讀者對象:數學專業的本科生、研究生和相關的科研人員。
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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