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|a 10.1007/978-981-99-3750-9
|2 doi
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|a (OCoLC)1396064746
|z (OCoLC)1395947497
|z (OCoLC)1396894014
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|a TA1637
|b .H4 2023
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|a HCDD
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|a He, Chuan.
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|a Parallel operator splitting algorithms with application to imaging inverse problems /
|c Chuan He, Changhua Hu.
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| 264 |
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|a Singapore :
|b Springer,
|c 2023.
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| 300 |
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|a 1 online resource (208 p.).
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| 336 |
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|a text
|b txt
|2 rdacontent
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|a computer
|b c
|2 rdamedia
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| 338 |
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|a online resource
|b cr
|2 rdacarrier
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| 490 |
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|a Advanced and Intelligent Manufacturing in China
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|a Intro -- Preface -- Contents -- About the Authors -- 1 Introduction -- 1.1 Implications for Image Restoration -- 1.2 Regularization Methods for Image Restoration -- 1.2.1 Image Degradation Mechanisms and Degradation Modeling -- 1.2.2 Regularization Methods Based on Variational Partial Differential Equations -- 1.2.3 Regularization Methods Based on Wavelet Frame Theory -- 1.2.4 Regularization Methods Based on Sparse Representation of Images -- 1.2.5 Random Field-Based Regularization Methods -- 1.3 Nonlinear Iterative Algorithm for Image Restoration -- 1.3.1 Traditional Methods
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|a 1.3.2 Operator Splitting Methods -- 1.3.3 Convergence Analysis of the Splitting Algorithms -- 1.3.4 Adaptive Estimation of the Regularization Parameter -- References -- 2 Mathematical Fundamentals -- 2.1 Summarize -- 2.2 Convolution -- 2.2.1 One-Dimensional Discrete Convolution -- 2.2.2 Two-Dimensional Discrete Convolution -- 2.3 Fourier Transform and Discrete Fourier Transform -- 2.4 Theory and Methods of Fixed-Points in Hilbert Spaces -- 2.4.1 Hilbert Space -- 2.4.2 Non-expansive Operators with Fixed-Point Iterations -- 2.4.3 Maximally Monotone Operator
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|a 2.4.4 Solution of the l1-ball Projection Problem -- Reference -- 3 Ill-Poseness of Imaging Inverse Problems and Regularization for Detail Preservation -- 3.1 Summarize -- 3.2 Typical Types of Image Blur -- 3.3 The Ill-Posed Nature of Image Deblurring -- 3.3.1 Discretization of Convolution Equations and Ill-Posed Analysis of Blur Matrices -- 3.3.2 Image Restoration Based on Inverse Filter -- 3.4 Tikhonov Image Regularization -- 3.4.1 Tikhonov Regularization Idea -- 3.4.2 Wiener Filtering -- 3.4.3 Constrained Least Square Filtering -- 3.5 Detail-Preserving Regularization for Image
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|a 3.5.1 Total Generalized Variational Regularization Model -- 3.5.2 Shearlet Regularization Model -- 3.6 Image Quality Evaluation -- References -- 4 Fast Parameter Estimation in TV-Based Image Restoration -- 4.1 Summarize -- 4.2 Overview of Adaptive Parameter Estimation Methods in TV Image Restoration -- 4.3 Fast Adaptive Parameter Estimation Based on ADMM and Discrepancy Principle -- 4.3.1 Augmented Lagrangian Model for TV Regularized Problem -- 4.3.2 Algorithm Derivation -- 4.3.3 Convergence Analysis -- 4.3.4 Parameter Settings -- 4.4 Extension of Fast Adaptive Parameter Estimation Algorithm
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|a 4.4.1 Equivalent Splitting Bregman Algorithm -- 4.4.2 Interval Constrained TV Image Restoration with Fast Adaptive Parameter Estimation -- 4.5 Experimental Results -- 4.5.1 Experiment 1: Implications for Significance Regularization Parameter Estimation -- 4.5.2 Experiment 2-Comparison with Other Adaptive Algorithms -- 4.5.3 Experiment 3-Comparison of Denoising Experiments -- References -- 5 Parallel Alternating Derection Method of Multipliers with Application to Image Restoration -- 5.1 Summarize -- 5.2 Parallel Alternating Direction Method of Multipliers
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|a 5.2.1 A General Description of the Regularized Image Restoration Objective Function
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|a Image denoising, image deblurring, image inpainting, super-resolution, and compressed sensing reconstruction have important application value in engineering practice, and they are also the hot frontiers in the field of image processing. This book focuses on the numerical analysis of ill condition of imaging inverse problems and the methods of solving imaging inverse problems based on operator splitting. Both algorithmic theory and numerical experiments have been addressed. The book is divided into six chapters, including preparatory knowledge, ill-condition numerical analysis and regularization method of imaging inverse problems, adaptive regularization parameter estimation, and parallel solution methods of imaging inverse problem based on operator splitting. Although the research methods in this book take image denoising, deblurring, inpainting, and compressed sensing reconstruction as examples, they can also be extended to image processing problems such as image segmentation, hyperspectral decomposition, and image compression. This book can benefit teachers and graduate students in colleges and universities, or be used as a reference for self-study or further study of image processing technology engineers. This book is a translation of an original German edition. The translation was done with the help of artificial intelligence (machine translation by the service DeepL.com). A subsequent human revision was done primarily in terms of content, so that the book will read stylistically differently from a conventional translation.
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| 504 |
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|a Includes bibliographical references and index.
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| 588 |
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|a Description based on online resource; title from digital title page (viewed on October 17, 2023).
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| 650 |
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|a Image processing
|x Data processing.
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| 650 |
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0 |
|a Algorithms.
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| 650 |
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7 |
|a algorithms.
|2 aat
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| 650 |
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7 |
|a Algorithms.
|2 fast
|0 (OCoLC)fst00805020
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| 650 |
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7 |
|a Image processing
|x Data processing.
|2 fast
|0 (OCoLC)fst00967506
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| 700 |
1 |
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|a Hu, Changhua.
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| 776 |
0 |
8 |
|i Print version:
|a He, Chuan
|t Parallel Operator Splitting Algorithms with Application to Imaging Inverse Problems
|d Singapore : Springer,c2023
|z 9789819937493
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| 830 |
|
0 |
|a Advanced and Intelligent Manufacturing in China.
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| 856 |
4 |
0 |
|u https://holycross.idm.oclc.org/login?auth=cas&url=https://link.springer.com/10.1007/978-981-99-3750-9
|y Click for online access
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| 903 |
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|a SPRING-ALL2023
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| 994 |
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|a 92
|b HCD
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