Parallel Operator Splitting Algorithms with Application to Imaging Inverse Problems

Parallel Operator Splitting Algorithms with Application to Imaging Inverse Problems

Author: Chuan He

Publisher: Springer Nature

Published: 2023-08-28

Total Pages: 208

ISBN-13: 9819937507

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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.


Book Synopsis Parallel Operator Splitting Algorithms with Application to Imaging Inverse Problems by : Chuan He

Download or read book Parallel Operator Splitting Algorithms with Application to Imaging Inverse Problems written by Chuan He and published by Springer Nature. This book was released on 2023-08-28 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Splitting Methods in Communication, Imaging, Science, and Engineering

Splitting Methods in Communication, Imaging, Science, and Engineering

Author: Roland Glowinski

Publisher: Springer

Published: 2017-01-05

Total Pages: 820

ISBN-13: 3319415891

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This book is about computational methods based on operator splitting. It consists of twenty-three chapters written by recognized splitting method contributors and practitioners, and covers a vast spectrum of topics and application areas, including computational mechanics, computational physics, image processing, wireless communication, nonlinear optics, and finance. Therefore, the book presents very versatile aspects of splitting methods and their applications, motivating the cross-fertilization of ideas.


Book Synopsis Splitting Methods in Communication, Imaging, Science, and Engineering by : Roland Glowinski

Download or read book Splitting Methods in Communication, Imaging, Science, and Engineering written by Roland Glowinski and published by Springer. This book was released on 2017-01-05 with total page 820 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is about computational methods based on operator splitting. It consists of twenty-three chapters written by recognized splitting method contributors and practitioners, and covers a vast spectrum of topics and application areas, including computational mechanics, computational physics, image processing, wireless communication, nonlinear optics, and finance. Therefore, the book presents very versatile aspects of splitting methods and their applications, motivating the cross-fertilization of ideas.

Iterative Optimization in Inverse Problems

Iterative Optimization in Inverse Problems

Author: Charles L. Byrne

Publisher: CRC Press

Published: 2014-02-12

Total Pages: 302

ISBN-13: 1482222337

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Iterative Optimization in Inverse Problems brings together a number of important iterative algorithms for medical imaging, optimization, and statistical estimation. It incorporates recent work that has not appeared in other books and draws on the author’s considerable research in the field, including his recently developed class of SUMMA algorithms. Related to sequential unconstrained minimization methods, the SUMMA class includes a wide range of iterative algorithms well known to researchers in various areas, such as statistics and image processing. Organizing the topics from general to more specific, the book first gives an overview of sequential optimization, the subclasses of auxiliary-function methods, and the SUMMA algorithms. The next three chapters present particular examples in more detail, including barrier- and penalty-function methods, proximal minimization, and forward-backward splitting. The author also focuses on fixed-point algorithms for operators on Euclidean space and then extends the discussion to include distance measures other than the usual Euclidean distance. In the final chapters, specific problems illustrate the use of iterative methods previously discussed. Most chapters contain exercises that introduce new ideas and make the book suitable for self-study. Unifying a variety of seemingly disparate algorithms, the book shows how to derive new properties of algorithms by comparing known properties of other algorithms. This unifying approach also helps researchers—from statisticians working on parameter estimation to image scientists processing scanning data to mathematicians involved in theoretical and applied optimization—discover useful related algorithms in areas outside of their expertise.


Book Synopsis Iterative Optimization in Inverse Problems by : Charles L. Byrne

Download or read book Iterative Optimization in Inverse Problems written by Charles L. Byrne and published by CRC Press. This book was released on 2014-02-12 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: Iterative Optimization in Inverse Problems brings together a number of important iterative algorithms for medical imaging, optimization, and statistical estimation. It incorporates recent work that has not appeared in other books and draws on the author’s considerable research in the field, including his recently developed class of SUMMA algorithms. Related to sequential unconstrained minimization methods, the SUMMA class includes a wide range of iterative algorithms well known to researchers in various areas, such as statistics and image processing. Organizing the topics from general to more specific, the book first gives an overview of sequential optimization, the subclasses of auxiliary-function methods, and the SUMMA algorithms. The next three chapters present particular examples in more detail, including barrier- and penalty-function methods, proximal minimization, and forward-backward splitting. The author also focuses on fixed-point algorithms for operators on Euclidean space and then extends the discussion to include distance measures other than the usual Euclidean distance. In the final chapters, specific problems illustrate the use of iterative methods previously discussed. Most chapters contain exercises that introduce new ideas and make the book suitable for self-study. Unifying a variety of seemingly disparate algorithms, the book shows how to derive new properties of algorithms by comparing known properties of other algorithms. This unifying approach also helps researchers—from statisticians working on parameter estimation to image scientists processing scanning data to mathematicians involved in theoretical and applied optimization—discover useful related algorithms in areas outside of their expertise.

Splitting Algorithms, Modern Operator Theory, and Applications

Splitting Algorithms, Modern Operator Theory, and Applications

Author: Heinz H. Bauschke

Publisher: Springer Nature

Published: 2019-11-06

Total Pages: 489

ISBN-13: 3030259390

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This book brings together research articles and state-of-the-art surveys in broad areas of optimization and numerical analysis with particular emphasis on algorithms. The discussion also focuses on advances in monotone operator theory and other topics from variational analysis and nonsmooth optimization, especially as they pertain to algorithms and concrete, implementable methods. The theory of monotone operators is a central framework for understanding and analyzing splitting algorithms. Topics discussed in the volume were presented at the interdisciplinary workshop titled Splitting Algorithms, Modern Operator Theory, and Applications held in Oaxaca, Mexico in September, 2017. Dedicated to Jonathan M. Borwein, one of the most versatile mathematicians in contemporary history, this compilation brings theory together with applications in novel and insightful ways.


Book Synopsis Splitting Algorithms, Modern Operator Theory, and Applications by : Heinz H. Bauschke

Download or read book Splitting Algorithms, Modern Operator Theory, and Applications written by Heinz H. Bauschke and published by Springer Nature. This book was released on 2019-11-06 with total page 489 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book brings together research articles and state-of-the-art surveys in broad areas of optimization and numerical analysis with particular emphasis on algorithms. The discussion also focuses on advances in monotone operator theory and other topics from variational analysis and nonsmooth optimization, especially as they pertain to algorithms and concrete, implementable methods. The theory of monotone operators is a central framework for understanding and analyzing splitting algorithms. Topics discussed in the volume were presented at the interdisciplinary workshop titled Splitting Algorithms, Modern Operator Theory, and Applications held in Oaxaca, Mexico in September, 2017. Dedicated to Jonathan M. Borwein, one of the most versatile mathematicians in contemporary history, this compilation brings theory together with applications in novel and insightful ways.

Introduction to Inverse Problems in Imaging

Introduction to Inverse Problems in Imaging

Author: M. Bertero

Publisher: CRC Press

Published: 2021-12-20

Total Pages: 358

ISBN-13: 1000516350

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Fully updated throughout and with several new chapters, this second edition of Introduction to Inverse Problems in Imaging guides advanced undergraduate and graduate students in physics, computer science, mathematics and engineering through the principles of linear inverse problems, in addition to methods of their approximate solution and their practical applications in imaging. This second edition contains new chapters on edge-preserving and sparsity-enforcing regularization in addition to maximum likelihood methods and Bayesian regularization for Poisson data. The level of mathematical treatment is kept as low as possible to make the book suitable for a wide range of students from different backgrounds, with readers needing just a rudimentary understanding of analysis, geometry, linear algebra, probability theory, and Fourier analysis. The authors concentrate on presenting easily implementable and fast solution algorithms, and this second edition is accompanied by numerical examples throughout. It will provide readers with the appropriate background needed for a clear understanding of the essence of inverse problems (ill-posedness and its cure) and, consequently, for an intelligent assessment of the rapidly growing literature on these problems. Key features: Provides an accessible introduction to the topic while keeping mathematics to a minimum Interdisciplinary topic with growing relevance and wide-ranging applications Accompanied by numerical examples throughout


Book Synopsis Introduction to Inverse Problems in Imaging by : M. Bertero

Download or read book Introduction to Inverse Problems in Imaging written by M. Bertero and published by CRC Press. This book was released on 2021-12-20 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fully updated throughout and with several new chapters, this second edition of Introduction to Inverse Problems in Imaging guides advanced undergraduate and graduate students in physics, computer science, mathematics and engineering through the principles of linear inverse problems, in addition to methods of their approximate solution and their practical applications in imaging. This second edition contains new chapters on edge-preserving and sparsity-enforcing regularization in addition to maximum likelihood methods and Bayesian regularization for Poisson data. The level of mathematical treatment is kept as low as possible to make the book suitable for a wide range of students from different backgrounds, with readers needing just a rudimentary understanding of analysis, geometry, linear algebra, probability theory, and Fourier analysis. The authors concentrate on presenting easily implementable and fast solution algorithms, and this second edition is accompanied by numerical examples throughout. It will provide readers with the appropriate background needed for a clear understanding of the essence of inverse problems (ill-posedness and its cure) and, consequently, for an intelligent assessment of the rapidly growing literature on these problems. Key features: Provides an accessible introduction to the topic while keeping mathematics to a minimum Interdisciplinary topic with growing relevance and wide-ranging applications Accompanied by numerical examples throughout

Fixed-Point Algorithms for Inverse Problems in Science and Engineering

Fixed-Point Algorithms for Inverse Problems in Science and Engineering

Author: Heinz H. Bauschke

Publisher: Springer Science & Business Media

Published: 2011-05-27

Total Pages: 409

ISBN-13: 1441995692

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"Fixed-Point Algorithms for Inverse Problems in Science and Engineering" presents some of the most recent work from top-notch researchers studying projection and other first-order fixed-point algorithms in several areas of mathematics and the applied sciences. The material presented provides a survey of the state-of-the-art theory and practice in fixed-point algorithms, identifying emerging problems driven by applications, and discussing new approaches for solving these problems. This book incorporates diverse perspectives from broad-ranging areas of research including, variational analysis, numerical linear algebra, biotechnology, materials science, computational solid-state physics, and chemistry. Topics presented include: Theory of Fixed-point algorithms: convex analysis, convex optimization, subdifferential calculus, nonsmooth analysis, proximal point methods, projection methods, resolvent and related fixed-point theoretic methods, and monotone operator theory. Numerical analysis of fixed-point algorithms: choice of step lengths, of weights, of blocks for block-iterative and parallel methods, and of relaxation parameters; regularization of ill-posed problems; numerical comparison of various methods. Areas of Applications: engineering (image and signal reconstruction and decompression problems), computer tomography and radiation treatment planning (convex feasibility problems), astronomy (adaptive optics), crystallography (molecular structure reconstruction), computational chemistry (molecular structure simulation) and other areas. Because of the variety of applications presented, this book can easily serve as a basis for new and innovated research and collaboration.


Book Synopsis Fixed-Point Algorithms for Inverse Problems in Science and Engineering by : Heinz H. Bauschke

Download or read book Fixed-Point Algorithms for Inverse Problems in Science and Engineering written by Heinz H. Bauschke and published by Springer Science & Business Media. This book was released on 2011-05-27 with total page 409 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Fixed-Point Algorithms for Inverse Problems in Science and Engineering" presents some of the most recent work from top-notch researchers studying projection and other first-order fixed-point algorithms in several areas of mathematics and the applied sciences. The material presented provides a survey of the state-of-the-art theory and practice in fixed-point algorithms, identifying emerging problems driven by applications, and discussing new approaches for solving these problems. This book incorporates diverse perspectives from broad-ranging areas of research including, variational analysis, numerical linear algebra, biotechnology, materials science, computational solid-state physics, and chemistry. Topics presented include: Theory of Fixed-point algorithms: convex analysis, convex optimization, subdifferential calculus, nonsmooth analysis, proximal point methods, projection methods, resolvent and related fixed-point theoretic methods, and monotone operator theory. Numerical analysis of fixed-point algorithms: choice of step lengths, of weights, of blocks for block-iterative and parallel methods, and of relaxation parameters; regularization of ill-posed problems; numerical comparison of various methods. Areas of Applications: engineering (image and signal reconstruction and decompression problems), computer tomography and radiation treatment planning (convex feasibility problems), astronomy (adaptive optics), crystallography (molecular structure reconstruction), computational chemistry (molecular structure simulation) and other areas. Because of the variety of applications presented, this book can easily serve as a basis for new and innovated research and collaboration.

Computational Methods for Inverse Problems in Imaging

Computational Methods for Inverse Problems in Imaging

Author: Marco Donatelli

Publisher: Springer Nature

Published: 2019-11-26

Total Pages: 171

ISBN-13: 3030328821

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This book presents recent mathematical methods in the area of inverse problems in imaging with a particular focus on the computational aspects and applications. The formulation of inverse problems in imaging requires accurate mathematical modeling in order to preserve the significant features of the image. The book describes computational methods to efficiently address these problems based on new optimization algorithms for smooth and nonsmooth convex minimization, on the use of structured (numerical) linear algebra, and on multilevel techniques. It also discusses various current and challenging applications in fields such as astronomy, microscopy, and biomedical imaging. The book is intended for researchers and advanced graduate students interested in inverse problems and imaging.


Book Synopsis Computational Methods for Inverse Problems in Imaging by : Marco Donatelli

Download or read book Computational Methods for Inverse Problems in Imaging written by Marco Donatelli and published by Springer Nature. This book was released on 2019-11-26 with total page 171 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents recent mathematical methods in the area of inverse problems in imaging with a particular focus on the computational aspects and applications. The formulation of inverse problems in imaging requires accurate mathematical modeling in order to preserve the significant features of the image. The book describes computational methods to efficiently address these problems based on new optimization algorithms for smooth and nonsmooth convex minimization, on the use of structured (numerical) linear algebra, and on multilevel techniques. It also discusses various current and challenging applications in fields such as astronomy, microscopy, and biomedical imaging. The book is intended for researchers and advanced graduate students interested in inverse problems and imaging.

Mathematical Methods in Image Processing and Inverse Problems

Mathematical Methods in Image Processing and Inverse Problems

Author: Xue-Cheng Tai

Publisher: Springer Nature

Published: 2021-09-25

Total Pages: 226

ISBN-13: 9811627010

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This book contains eleven original and survey scientific research articles arose from presentations given by invited speakers at International Workshop on Image Processing and Inverse Problems, held in Beijing Computational Science Research Center, Beijing, China, April 21–24, 2018. The book was dedicated to Professor Raymond Chan on the occasion of his 60th birthday. The contents of the book cover topics including image reconstruction, image segmentation, image registration, inverse problems and so on. Deep learning, PDE, statistical theory based research methods and techniques were discussed. The state-of-the-art developments on mathematical analysis, advanced modeling, efficient algorithm and applications were presented. The collected papers in this book also give new research trends in deep learning and optimization for imaging science. It should be a good reference for researchers working on related problems, as well as for researchers working on computer vision and visualization, inverse problems, image processing and medical imaging.


Book Synopsis Mathematical Methods in Image Processing and Inverse Problems by : Xue-Cheng Tai

Download or read book Mathematical Methods in Image Processing and Inverse Problems written by Xue-Cheng Tai and published by Springer Nature. This book was released on 2021-09-25 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains eleven original and survey scientific research articles arose from presentations given by invited speakers at International Workshop on Image Processing and Inverse Problems, held in Beijing Computational Science Research Center, Beijing, China, April 21–24, 2018. The book was dedicated to Professor Raymond Chan on the occasion of his 60th birthday. The contents of the book cover topics including image reconstruction, image segmentation, image registration, inverse problems and so on. Deep learning, PDE, statistical theory based research methods and techniques were discussed. The state-of-the-art developments on mathematical analysis, advanced modeling, efficient algorithm and applications were presented. The collected papers in this book also give new research trends in deep learning and optimization for imaging science. It should be a good reference for researchers working on related problems, as well as for researchers working on computer vision and visualization, inverse problems, image processing and medical imaging.

Discrete Geometry for Computer Imagery

Discrete Geometry for Computer Imagery

Author: Nicolas Normand

Publisher: Springer

Published: 2016-04-08

Total Pages: 453

ISBN-13: 3319323601

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This book constitutes the refereed proceedings of the 19th IAPR International Conference on Discrete Geometry for Computer Imagery, DGCI 2016, held in Nantes, France, in April 2016. The 32 revised full papers presented together with 2 invited talks were carefully selected from 51 submissions. The papers are organized in topical sections on combinatorial tools; discretization; discrete tomography; discrete and combinatorial topology; shape descriptors; models for discrete geometry; circle drawing; morphological analysis; geometric transforms; and discrete shape representation, recognition and analysis.


Book Synopsis Discrete Geometry for Computer Imagery by : Nicolas Normand

Download or read book Discrete Geometry for Computer Imagery written by Nicolas Normand and published by Springer. This book was released on 2016-04-08 with total page 453 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 19th IAPR International Conference on Discrete Geometry for Computer Imagery, DGCI 2016, held in Nantes, France, in April 2016. The 32 revised full papers presented together with 2 invited talks were carefully selected from 51 submissions. The papers are organized in topical sections on combinatorial tools; discretization; discrete tomography; discrete and combinatorial topology; shape descriptors; models for discrete geometry; circle drawing; morphological analysis; geometric transforms; and discrete shape representation, recognition and analysis.

Large-Scale and Distributed Optimization

Large-Scale and Distributed Optimization

Author: Pontus Giselsson

Publisher: Springer

Published: 2018-11-11

Total Pages: 412

ISBN-13: 3319974785

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This book presents tools and methods for large-scale and distributed optimization. Since many methods in "Big Data" fields rely on solving large-scale optimization problems, often in distributed fashion, this topic has over the last decade emerged to become very important. As well as specific coverage of this active research field, the book serves as a powerful source of information for practitioners as well as theoreticians. Large-Scale and Distributed Optimization is a unique combination of contributions from leading experts in the field, who were speakers at the LCCC Focus Period on Large-Scale and Distributed Optimization, held in Lund, 14th–16th June 2017. A source of information and innovative ideas for current and future research, this book will appeal to researchers, academics, and students who are interested in large-scale optimization.


Book Synopsis Large-Scale and Distributed Optimization by : Pontus Giselsson

Download or read book Large-Scale and Distributed Optimization written by Pontus Giselsson and published by Springer. This book was released on 2018-11-11 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents tools and methods for large-scale and distributed optimization. Since many methods in "Big Data" fields rely on solving large-scale optimization problems, often in distributed fashion, this topic has over the last decade emerged to become very important. As well as specific coverage of this active research field, the book serves as a powerful source of information for practitioners as well as theoreticians. Large-Scale and Distributed Optimization is a unique combination of contributions from leading experts in the field, who were speakers at the LCCC Focus Period on Large-Scale and Distributed Optimization, held in Lund, 14th–16th June 2017. A source of information and innovative ideas for current and future research, this book will appeal to researchers, academics, and students who are interested in large-scale optimization.