First Order Convex Optimization Methods For Signal And Image Processing

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First-Order Methods in Optimization

Author : Amir Beck
Publisher : SIAM
ISBN 13 : 1611974984
Total Pages : 476 pages
Book Rating : 4.6/5 (119 download)

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Book Synopsis First-Order Methods in Optimization by : Amir Beck

Download or read book First-Order Methods in Optimization written by Amir Beck and published by SIAM. This book was released on 2017-10-02 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt: The primary goal of this book is to provide a self-contained, comprehensive study of the main ?rst-order methods that are frequently used in solving large-scale problems. First-order methods exploit information on values and gradients/subgradients (but not Hessians) of the functions composing the model under consideration. With the increase in the number of applications that can be modeled as large or even huge-scale optimization problems, there has been a revived interest in using simple methods that require low iteration cost as well as low memory storage. The author has gathered, reorganized, and synthesized (in a unified manner) many results that are currently scattered throughout the literature, many of which cannot be typically found in optimization books. First-Order Methods in Optimization offers comprehensive study of first-order methods with the theoretical foundations; provides plentiful examples and illustrations; emphasizes rates of convergence and complexity analysis of the main first-order methods used to solve large-scale problems; and covers both variables and functional decomposition methods.

Handbook of Convex Optimization Methods in Imaging Science

Author : Vishal Monga
Publisher : Springer
ISBN 13 : 3319616099
Total Pages : 238 pages
Book Rating : 4.3/5 (196 download)

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Book Synopsis Handbook of Convex Optimization Methods in Imaging Science by : Vishal Monga

Download or read book Handbook of Convex Optimization Methods in Imaging Science written by Vishal Monga and published by Springer. This book was released on 2017-10-27 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers recent advances in image processing and imaging sciences from an optimization viewpoint, especially convex optimization with the goal of designing tractable algorithms. Throughout the handbook, the authors introduce topics on the most key aspects of image acquisition and processing that are based on the formulation and solution of novel optimization problems. The first part includes a review of the mathematical methods and foundations required, and covers topics in image quality optimization and assessment. The second part of the book discusses concepts in image formation and capture from color imaging to radar and multispectral imaging. The third part focuses on sparsity constrained optimization in image processing and vision and includes inverse problems such as image restoration and de-noising, image classification and recognition and learning-based problems pertinent to image understanding. Throughout, convex optimization techniques are shown to be a critically important mathematical tool for imaging science problems and applied extensively. Convex Optimization Methods in Imaging Science is the first book of its kind and will appeal to undergraduate and graduate students, industrial researchers and engineers and those generally interested in computational aspects of modern, real-world imaging and image processing problems.

Convex Analysis and Monotone Operator Theory in Hilbert Spaces

Author : Heinz H. Bauschke
Publisher : Springer
ISBN 13 : 3319483110
Total Pages : 624 pages
Book Rating : 4.3/5 (194 download)

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Book Synopsis Convex Analysis and Monotone Operator Theory in Hilbert Spaces by : Heinz H. Bauschke

Download or read book Convex Analysis and Monotone Operator Theory in Hilbert Spaces written by Heinz H. Bauschke and published by Springer. This book was released on 2017-02-28 with total page 624 pages. Available in PDF, EPUB and Kindle. Book excerpt: This reference text, now in its second edition, offers a modern unifying presentation of three basic areas of nonlinear analysis: convex analysis, monotone operator theory, and the fixed point theory of nonexpansive operators. Taking a unique comprehensive approach, the theory is developed from the ground up, with the rich connections and interactions between the areas as the central focus, and it is illustrated by a large number of examples. The Hilbert space setting of the material offers a wide range of applications while avoiding the technical difficulties of general Banach spaces. The authors have also drawn upon recent advances and modern tools to simplify the proofs of key results making the book more accessible to a broader range of scholars and users. Combining a strong emphasis on applications with exceptionally lucid writing and an abundance of exercises, this text is of great value to a large audience including pure and applied mathematicians as well as researchers in engineering, data science, machine learning, physics, decision sciences, economics, and inverse problems. The second edition of Convex Analysis and Monotone Operator Theory in Hilbert Spaces greatly expands on the first edition, containing over 140 pages of new material, over 270 new results, and more than 100 new exercises. It features a new chapter on proximity operators including two sections on proximity operators of matrix functions, in addition to several new sections distributed throughout the original chapters. Many existing results have been improved, and the list of references has been updated. Heinz H. Bauschke is a Full Professor of Mathematics at the Kelowna campus of the University of British Columbia, Canada. Patrick L. Combettes, IEEE Fellow, was on the faculty of the City University of New York and of Université Pierre et Marie Curie – Paris 6 before joining North Carolina State University as a Distinguished Professor of Mathematics in 2016.

Convex Optimization for Signal Processing and Communications

Author : Chong-Yung Chi
Publisher : CRC Press
ISBN 13 : 1315349809
Total Pages : 294 pages
Book Rating : 4.3/5 (153 download)

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Book Synopsis Convex Optimization for Signal Processing and Communications by : Chong-Yung Chi

Download or read book Convex Optimization for Signal Processing and Communications written by Chong-Yung Chi and published by CRC Press. This book was released on 2017-01-24 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: Convex Optimization for Signal Processing and Communications: From Fundamentals to Applications provides fundamental background knowledge of convex optimization, while striking a balance between mathematical theory and applications in signal processing and communications. In addition to comprehensive proofs and perspective interpretations for core convex optimization theory, this book also provides many insightful figures, remarks, illustrative examples, and guided journeys from theory to cutting-edge research explorations, for efficient and in-depth learning, especially for engineering students and professionals. With the powerful convex optimization theory and tools, this book provides you with a new degree of freedom and the capability of solving challenging real-world scientific and engineering problems.

First-Order Methods in Optimization

Author : Amir Beck
Publisher : SIAM
ISBN 13 : 1611974992
Total Pages : 487 pages
Book Rating : 4.6/5 (119 download)

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Book Synopsis First-Order Methods in Optimization by : Amir Beck

Download or read book First-Order Methods in Optimization written by Amir Beck and published by SIAM. This book was released on 2017-10-02 with total page 487 pages. Available in PDF, EPUB and Kindle. Book excerpt: The primary goal of this book is to provide a self-contained, comprehensive study of the main ?rst-order methods that are frequently used in solving large-scale problems. First-order methods exploit information on values and gradients/subgradients (but not Hessians) of the functions composing the model under consideration. With the increase in the number of applications that can be modeled as large or even huge-scale optimization problems, there has been a revived interest in using simple methods that require low iteration cost as well as low memory storage. The author has gathered, reorganized, and synthesized (in a unified manner) many results that are currently scattered throughout the literature, many of which cannot be typically found in optimization books. First-Order Methods in Optimization offers comprehensive study of first-order methods with the theoretical foundations; provides plentiful examples and illustrations; emphasizes rates of convergence and complexity analysis of the main first-order methods used to solve large-scale problems; and covers both variables and functional decomposition methods.

Convex Optimization

Author : Sébastien Bubeck
Publisher : Foundations and Trends (R) in Machine Learning
ISBN 13 : 9781601988607
Total Pages : 142 pages
Book Rating : 4.9/5 (886 download)

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Book Synopsis Convex Optimization by : Sébastien Bubeck

Download or read book Convex Optimization written by Sébastien Bubeck and published by Foundations and Trends (R) in Machine Learning. This book was released on 2015-11-12 with total page 142 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph presents the main complexity theorems in convex optimization and their corresponding algorithms. It begins with the fundamental theory of black-box optimization and proceeds to guide the reader through recent advances in structural optimization and stochastic optimization. The presentation of black-box optimization, strongly influenced by the seminal book by Nesterov, includes the analysis of cutting plane methods, as well as (accelerated) gradient descent schemes. Special attention is also given to non-Euclidean settings (relevant algorithms include Frank-Wolfe, mirror descent, and dual averaging), and discussing their relevance in machine learning. The text provides a gentle introduction to structural optimization with FISTA (to optimize a sum of a smooth and a simple non-smooth term), saddle-point mirror prox (Nemirovski's alternative to Nesterov's smoothing), and a concise description of interior point methods. In stochastic optimization it discusses stochastic gradient descent, mini-batches, random coordinate descent, and sublinear algorithms. It also briefly touches upon convex relaxation of combinatorial problems and the use of randomness to round solutions, as well as random walks based methods.

Proximal Algorithms

Author : Neal Parikh
Publisher : Now Pub
ISBN 13 : 9781601987167
Total Pages : 130 pages
Book Rating : 4.9/5 (871 download)

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Book Synopsis Proximal Algorithms by : Neal Parikh

Download or read book Proximal Algorithms written by Neal Parikh and published by Now Pub. This book was released on 2013-11 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proximal Algorithms discusses proximal operators and proximal algorithms, and illustrates their applicability to standard and distributed convex optimization in general and many applications of recent interest in particular. Much like Newton's method is a standard tool for solving unconstrained smooth optimization problems of modest size, proximal algorithms can be viewed as an analogous tool for nonsmooth, constrained, large-scale, or distributed versions of these problems. They are very generally applicable, but are especially well-suited to problems of substantial recent interest involving large or high-dimensional datasets. Proximal methods sit at a higher level of abstraction than classical algorithms like Newton's method: the base operation is evaluating the proximal operator of a function, which itself involves solving a small convex optimization problem. These subproblems, which generalize the problem of projecting a point onto a convex set, often admit closed-form solutions or can be solved very quickly with standard or simple specialized methods. Proximal Algorithms discusses different interpretations of proximal operators and algorithms, looks at their connections to many other topics in optimization and applied mathematics, surveys some popular algorithms, and provides a large number of examples of proximal operators that commonly arise in practice.

Convex Optimization

Author : Stephen P. Boyd
Publisher : Cambridge University Press
ISBN 13 : 9780521833783
Total Pages : 744 pages
Book Rating : 4.8/5 (337 download)

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Book Synopsis Convex Optimization by : Stephen P. Boyd

Download or read book Convex Optimization written by Stephen P. Boyd and published by Cambridge University Press. This book was released on 2004-03-08 with total page 744 pages. Available in PDF, EPUB and Kindle. Book excerpt: Convex optimization problems arise frequently in many different fields. This book provides a comprehensive introduction to the subject, and shows in detail how such problems can be solved numerically with great efficiency. The book begins with the basic elements of convex sets and functions, and then describes various classes of convex optimization problems. Duality and approximation techniques are then covered, as are statistical estimation techniques. Various geometrical problems are then presented, and there is detailed discussion of unconstrained and constrained minimization problems, and interior-point methods. The focus of the book is on recognizing convex optimization problems and then finding the most appropriate technique for solving them. It contains many worked examples and homework exercises and will appeal to students, researchers and practitioners in fields such as engineering, computer science, mathematics, statistics, finance and economics.

Prediction, Learning, and Games

Author : Nicolo Cesa-Bianchi
Publisher : Cambridge University Press
ISBN 13 : 113945482X
Total Pages : 4 pages
Book Rating : 4.1/5 (394 download)

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Book Synopsis Prediction, Learning, and Games by : Nicolo Cesa-Bianchi

Download or read book Prediction, Learning, and Games written by Nicolo Cesa-Bianchi and published by Cambridge University Press. This book was released on 2006-03-13 with total page 4 pages. Available in PDF, EPUB and Kindle. Book excerpt: This important text and reference for researchers and students in machine learning, game theory, statistics and information theory offers a comprehensive treatment of the problem of predicting individual sequences. Unlike standard statistical approaches to forecasting, prediction of individual sequences does not impose any probabilistic assumption on the data-generating mechanism. Yet, prediction algorithms can be constructed that work well for all possible sequences, in the sense that their performance is always nearly as good as the best forecasting strategy in a given reference class. The central theme is the model of prediction using expert advice, a general framework within which many related problems can be cast and discussed. Repeated game playing, adaptive data compression, sequential investment in the stock market, sequential pattern analysis, and several other problems are viewed as instances of the experts' framework and analyzed from a common nonstochastic standpoint that often reveals new and intriguing connections.

Image and Signal Processing

Author : Abderrahim Elmoataz
Publisher : Springer
ISBN 13 : 3319079980
Total Pages : 694 pages
Book Rating : 4.3/5 (19 download)

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Book Synopsis Image and Signal Processing by : Abderrahim Elmoataz

Download or read book Image and Signal Processing written by Abderrahim Elmoataz and published by Springer. This book was released on 2014-06-04 with total page 694 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 6th International Conference, ICISP 2014, held in June/July 2014 in Cherbourg, France. The 76 revised full papers were carefully reviewed and selected from 164 submissions. The contributions are organized in topical sections on multispectral colour science, color imaging and applications, digital cultural heritage, document image analysis, graph-based representations, image filtering and representation, computer vision and pattern recognition, computer graphics, biomedical, and signal processing.

Convex Optimization in Signal Processing and Communications

Author : Daniel P. Palomar
Publisher : Cambridge University Press
ISBN 13 : 0521762227
Total Pages : 513 pages
Book Rating : 4.5/5 (217 download)

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Book Synopsis Convex Optimization in Signal Processing and Communications by : Daniel P. Palomar

Download or read book Convex Optimization in Signal Processing and Communications written by Daniel P. Palomar and published by Cambridge University Press. This book was released on 2010 with total page 513 pages. Available in PDF, EPUB and Kindle. Book excerpt: Leading experts provide the theoretical underpinnings of the subject plus tutorials on a wide range of applications, from automatic code generation to robust broadband beamforming. Emphasis on cutting-edge research and formulating problems in convex form make this an ideal textbook for advanced graduate courses and a useful self-study guide.

Handbook of Robust Low-Rank and Sparse Matrix Decomposition

Author : Thierry Bouwmans
Publisher : CRC Press
ISBN 13 : 1315353539
Total Pages : 510 pages
Book Rating : 4.3/5 (153 download)

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Book Synopsis Handbook of Robust Low-Rank and Sparse Matrix Decomposition by : Thierry Bouwmans

Download or read book Handbook of Robust Low-Rank and Sparse Matrix Decomposition written by Thierry Bouwmans and published by CRC Press. This book was released on 2016-09-20 with total page 510 pages. Available in PDF, EPUB and Kindle. Book excerpt: Handbook of Robust Low-Rank and Sparse Matrix Decomposition: Applications in Image and Video Processing shows you how robust subspace learning and tracking by decomposition into low-rank and sparse matrices provide a suitable framework for computer vision applications. Incorporating both existing and new ideas, the book conveniently gives you one-stop access to a number of different decompositions, algorithms, implementations, and benchmarking techniques. Divided into five parts, the book begins with an overall introduction to robust principal component analysis (PCA) via decomposition into low-rank and sparse matrices. The second part addresses robust matrix factorization/completion problems while the third part focuses on robust online subspace estimation, learning, and tracking. Covering applications in image and video processing, the fourth part discusses image analysis, image denoising, motion saliency detection, video coding, key frame extraction, and hyperspectral video processing. The final part presents resources and applications in background/foreground separation for video surveillance. With contributions from leading teams around the world, this handbook provides a complete overview of the concepts, theories, algorithms, and applications related to robust low-rank and sparse matrix decompositions. It is designed for researchers, developers, and graduate students in computer vision, image and video processing, real-time architecture, machine learning, and data mining.

First-order and Stochastic Optimization Methods for Machine Learning

Author : Guanghui Lan
Publisher : Springer Nature
ISBN 13 : 3030395685
Total Pages : 591 pages
Book Rating : 4.0/5 (33 download)

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Book Synopsis First-order and Stochastic Optimization Methods for Machine Learning by : Guanghui Lan

Download or read book First-order and Stochastic Optimization Methods for Machine Learning written by Guanghui Lan and published by Springer Nature. This book was released on 2020-05-15 with total page 591 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers not only foundational materials but also the most recent progresses made during the past few years on the area of machine learning algorithms. In spite of the intensive research and development in this area, there does not exist a systematic treatment to introduce the fundamental concepts and recent progresses on machine learning algorithms, especially on those based on stochastic optimization methods, randomized algorithms, nonconvex optimization, distributed and online learning, and projection free methods. This book will benefit the broad audience in the area of machine learning, artificial intelligence and mathematical programming community by presenting these recent developments in a tutorial style, starting from the basic building blocks to the most carefully designed and complicated algorithms for machine learning.

Handbook of Mathematical Models and Algorithms in Computer Vision and Imaging

Author : Ke Chen
Publisher : Springer Nature
ISBN 13 : 3030986616
Total Pages : 1981 pages
Book Rating : 4.0/5 (39 download)

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Book Synopsis Handbook of Mathematical Models and Algorithms in Computer Vision and Imaging by : Ke Chen

Download or read book Handbook of Mathematical Models and Algorithms in Computer Vision and Imaging written by Ke Chen and published by Springer Nature. This book was released on 2023-02-24 with total page 1981 pages. Available in PDF, EPUB and Kindle. Book excerpt: This handbook gathers together the state of the art on mathematical models and algorithms for imaging and vision. Its emphasis lies on rigorous mathematical methods, which represent the optimal solutions to a class of imaging and vision problems, and on effective algorithms, which are necessary for the methods to be translated to practical use in various applications. Viewing discrete images as data sampled from functional surfaces enables the use of advanced tools from calculus, functions and calculus of variations, and nonlinear optimization, and provides the basis of high-resolution imaging through geometry and variational models. Besides, optimization naturally connects traditional model-driven approaches to the emerging data-driven approaches of machine and deep learning. No other framework can provide comparable accuracy and precision to imaging and vision. Written by leading researchers in imaging and vision, the chapters in this handbook all start with gentle introductions, which make this work accessible to graduate students. For newcomers to the field, the book provides a comprehensive and fast-track introduction to the content, to save time and get on with tackling new and emerging challenges. For researchers, exposure to the state of the art of research works leads to an overall view of the entire field so as to guide new research directions and avoid pitfalls in moving the field forward and looking into the next decades of imaging and information services. This work can greatly benefit graduate students, researchers, and practitioners in imaging and vision; applied mathematicians; medical imagers; engineers; and computer scientists.

Sparse Image and Signal Processing

Author : Jean-Luc Starck
Publisher : Cambridge University Press
ISBN 13 : 1316483304
Total Pages : 449 pages
Book Rating : 4.3/5 (164 download)

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Book Synopsis Sparse Image and Signal Processing by : Jean-Luc Starck

Download or read book Sparse Image and Signal Processing written by Jean-Luc Starck and published by Cambridge University Press. This book was released on 2015-10-14 with total page 449 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thoroughly updated new edition presents state-of-the-art sparse and multiscale image and signal processing. It covers linear multiscale geometric transforms, such as wavelet, ridgelet, or curvelet transforms, and non-linear multiscale transforms based on the median and mathematical morphology operators. Along with an up-to-the-minute description of required computation, it covers the latest results in inverse problem solving and regularization, sparse signal decomposition, blind source separation, in-painting, and compressed sensing. New chapters and sections cover multiscale geometric transforms for three-dimensional data (data cubes), data on the sphere (geo-located data), dictionary learning, and nonnegative matrix factorization. The authors wed theory and practice in examining applications in areas such as astronomy, including recent results from the European Space Agency's Herschel mission, biology, fusion physics, cold dark matter simulation, medical MRI, digital media, and forensics. MATLAB® and IDL code, available online at www.SparseSignalRecipes.info, accompany these methods and all applications.

Inference and Learning from Data

Author : Ali H. Sayed
Publisher : Cambridge University Press
ISBN 13 : 1009218123
Total Pages : 1105 pages
Book Rating : 4.0/5 (92 download)

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Book Synopsis Inference and Learning from Data by : Ali H. Sayed

Download or read book Inference and Learning from Data written by Ali H. Sayed and published by Cambridge University Press. This book was released on 2022-11-30 with total page 1105 pages. Available in PDF, EPUB and Kindle. Book excerpt: Discover core topics in inference and learning with the first volume of this extraordinary three-volume set.

Introductory Lectures on Convex Optimization

Author : Y. Nesterov
Publisher : Springer Science & Business Media
ISBN 13 : 144198853X
Total Pages : 253 pages
Book Rating : 4.4/5 (419 download)

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Book Synopsis Introductory Lectures on Convex Optimization by : Y. Nesterov

Download or read book Introductory Lectures on Convex Optimization written by Y. Nesterov and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 253 pages. Available in PDF, EPUB and Kindle. Book excerpt: It was in the middle of the 1980s, when the seminal paper by Kar markar opened a new epoch in nonlinear optimization. The importance of this paper, containing a new polynomial-time algorithm for linear op timization problems, was not only in its complexity bound. At that time, the most surprising feature of this algorithm was that the theoretical pre diction of its high efficiency was supported by excellent computational results. This unusual fact dramatically changed the style and direc tions of the research in nonlinear optimization. Thereafter it became more and more common that the new methods were provided with a complexity analysis, which was considered a better justification of their efficiency than computational experiments. In a new rapidly develop ing field, which got the name "polynomial-time interior-point methods", such a justification was obligatory. Afteralmost fifteen years of intensive research, the main results of this development started to appear in monographs [12, 14, 16, 17, 18, 19]. Approximately at that time the author was asked to prepare a new course on nonlinear optimization for graduate students. The idea was to create a course which would reflect the new developments in the field. Actually, this was a major challenge. At the time only the theory of interior-point methods for linear optimization was polished enough to be explained to students. The general theory of self-concordant functions had appeared in print only once in the form of research monograph [12].