Fixed Point Algorithms For Inverse Problems In Science And Engineering

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Fixed-Point Algorithms for Inverse Problems in Science and Engineering

Heinz H. Bauschke,Regina S. Burachik,Patrick L. Combettes,Veit Elser,D. Russell Luke,Henry Wolkowicz
Fixed Point Algorithms for Inverse Problems in Science and Engineering Book PDF

Author : Heinz H. Bauschke,Regina S. Burachik,Patrick L. Combettes,Veit Elser,D. Russell Luke,Henry Wolkowicz
Publisher : Springer Science & Business Media
Page : 404 pages
File Size : 45,8 Mb
Release : 2011-05-27
Category : Mathematics
ISBN : 9781441995698

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Fixed-Point Algorithms for Inverse Problems in Science and Engineering by Heinz H. Bauschke,Regina S. Burachik,Patrick L. Combettes,Veit Elser,D. Russell Luke,Henry Wolkowicz Pdf

"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.

Parallel Operator Splitting Algorithms with Application to Imaging Inverse Problems

Chuan He,Changhua Hu
Parallel Operator Splitting Algorithms with Application to Imaging Inverse Problems Book PDF

Author : Chuan He,Changhua Hu
Publisher : Springer Nature
Page : 208 pages
File Size : 42,6 Mb
Release : 2023-08-28
Category : Computers
ISBN : 9789819937509

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Parallel Operator Splitting Algorithms with Application to Imaging Inverse Problems by Chuan He,Changhua Hu Pdf

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.

Inference and Learning from Data: Volume 1

Ali H. Sayed
Inference and Learning from Data Volume 1 Book PDF

Author : Ali H. Sayed
Publisher : Cambridge University Press
Page : 1106 pages
File Size : 45,5 Mb
Release : 2022-12-22
Category : Technology & Engineering
ISBN : 9781009218139

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Inference and Learning from Data: Volume 1 by Ali H. Sayed Pdf

This extraordinary three-volume work, written in an engaging and rigorous style by a world authority in the field, provides an accessible, comprehensive introduction to the full spectrum of mathematical and statistical techniques underpinning contemporary methods in data-driven learning and inference. This first volume, Foundations, introduces core topics in inference and learning, such as matrix theory, linear algebra, random variables, convex optimization and stochastic optimization, and prepares students for studying their practical application in later volumes. A consistent structure and pedagogy is employed throughout this volume to reinforce student understanding, with over 600 end-of-chapter problems (including solutions for instructors), 100 figures, 180 solved examples, datasets and downloadable Matlab code. Supported by sister volumes Inference and Learning, and unique in its scale and depth, this textbook sequence is ideal for early-career researchers and graduate students across many courses in signal processing, machine learning, statistical analysis, data science and inference.

Splitting Algorithms, Modern Operator Theory, and Applications

Heinz H. Bauschke,Regina S. Burachik,D. Russell Luke
Splitting Algorithms Modern Operator Theory and Applications Book PDF

Author : Heinz H. Bauschke,Regina S. Burachik,D. Russell Luke
Publisher : Springer Nature
Page : 489 pages
File Size : 51,9 Mb
Release : 2019-11-06
Category : Mathematics
ISBN : 9783030259396

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Splitting Algorithms, Modern Operator Theory, and Applications by Heinz H. Bauschke,Regina S. Burachik,D. Russell Luke Pdf

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.

Sparse Image and Signal Processing

Jean-Luc Starck,Fionn Murtagh,Jalal Fadili
Sparse Image and Signal Processing Book PDF

Author : Jean-Luc Starck,Fionn Murtagh,Jalal Fadili
Publisher : Cambridge University Press
Page : 449 pages
File Size : 40,7 Mb
Release : 2015-10-14
Category : Computers
ISBN : 9781107088061

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Sparse Image and Signal Processing by Jean-Luc Starck,Fionn Murtagh,Jalal Fadili Pdf

Presents state-of-the-art sparse and multiscale image and signal processing with applications in astronomy, biology, MRI, media, and forensics.

Large-Scale Convex Optimization

Ernest K. Ryu,Wotao Yin
Large Scale Convex Optimization Book PDF

Author : Ernest K. Ryu,Wotao Yin
Publisher : Cambridge University Press
Page : 320 pages
File Size : 44,8 Mb
Release : 2022-12-01
Category : Mathematics
ISBN : 9781009191067

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Large-Scale Convex Optimization by Ernest K. Ryu,Wotao Yin Pdf

Starting from where a first course in convex optimization leaves off, this text presents a unified analysis of first-order optimization methods – including parallel-distributed algorithms – through the abstraction of monotone operators. With the increased computational power and availability of big data over the past decade, applied disciplines have demanded that larger and larger optimization problems be solved. This text covers the first-order convex optimization methods that are uniquely effective at solving these large-scale optimization problems. Readers will have the opportunity to construct and analyze many well-known classical and modern algorithms using monotone operators, and walk away with a solid understanding of the diverse optimization algorithms. Graduate students and researchers in mathematical optimization, operations research, electrical engineering, statistics, and computer science will appreciate this concise introduction to the theory of convex optimization algorithms.

Computational Mathematics and Variational Analysis

Nicholas J. Daras,Themistocles M. Rassias
Computational Mathematics and Variational Analysis Book PDF

Author : Nicholas J. Daras,Themistocles M. Rassias
Publisher : Springer Nature
Page : 564 pages
File Size : 54,6 Mb
Release : 2020-06-06
Category : Mathematics
ISBN : 9783030446253

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Computational Mathematics and Variational Analysis by Nicholas J. Daras,Themistocles M. Rassias Pdf

This volume presents a broad discussion of computational methods and theories on various classical and modern research problems from pure and applied mathematics. Readers conducting research in mathematics, engineering, physics, and economics will benefit from the diversity of topics covered. Contributions from an international community treat the following subjects: calculus of variations, optimization theory, operations research, game theory, differential equations, functional analysis, operator theory, approximation theory, numerical analysis, asymptotic analysis, and engineering. Specific topics include algorithms for difference of monotone operators, variational inequalities in semi-inner product spaces, function variation principles and normed minimizers, equilibria of parametrized N-player nonlinear games, multi-symplectic numerical schemes for differential equations, time-delay multi-agent systems, computational methods in non-linear design of experiments, unsupervised stochastic learning, asymptotic statistical results, global-local transformation, scattering relations of elastic waves, generalized Ostrowski and trapezoid type rules, numerical approximation, Szász Durrmeyer operators and approximation, integral inequalities, behaviour of the solutions of functional equations, functional inequalities in complex Banach spaces, functional contractions in metric spaces.

Academic Press Library in Signal Processing

Paulo S.R. Diniz,Patrick A. Naylor,Johan Suykens
Academic Press Library in Signal Processing Book PDF

Author : Paulo S.R. Diniz,Patrick A. Naylor,Johan Suykens
Publisher : Academic Press
Page : 1559 pages
File Size : 54,6 Mb
Release : 2013-09-21
Category : Technology & Engineering
ISBN : 9780123972262

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Academic Press Library in Signal Processing by Paulo S.R. Diniz,Patrick A. Naylor,Johan Suykens Pdf

This first volume, edited and authored by world leading experts, gives a review of the principles, methods and techniques of important and emerging research topics and technologies in machine learning and advanced signal processing theory. With this reference source you will: Quickly grasp a new area of research Understand the underlying principles of a topic and its application Ascertain how a topic relates to other areas and learn of the research issues yet to be resolved Quick tutorial reviews of important and emerging topics of research in machine learning Presents core principles in signal processing theory and shows their applications Reference content on core principles, technologies, algorithms and applications Comprehensive references to journal articles and other literature on which to build further, more specific and detailed knowledge Edited by leading people in the field who, through their reputation, have been able to commission experts to write on a particular topic

Artificial Intelligence and Soft Computing

Leszek Rutkowski,Marcin Korytkowski,Rafał Scherer,Ryszard Tadeusiewicz,Lotfi Zadeh,Jacek Zurada
Artificial Intelligence and Soft Computing Book PDF

Author : Leszek Rutkowski,Marcin Korytkowski,Rafał Scherer,Ryszard Tadeusiewicz,Lotfi Zadeh,Jacek Zurada
Publisher : Springer
Page : 720 pages
File Size : 42,6 Mb
Release : 2012-04-17
Category : Computers
ISBN : 9783642293504

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Artificial Intelligence and Soft Computing by Leszek Rutkowski,Marcin Korytkowski,Rafał Scherer,Ryszard Tadeusiewicz,Lotfi Zadeh,Jacek Zurada Pdf

The two-volume set LNAI 7267 and 7268 (together with LNCS 7269 ) constitutes the refereed proceedings of the 11th International Conference on Artificial Intelligence and Soft Computing, ICAISC 2012, held in Zakopane, Poland in April/ May 2012. The 212 revised full papers presented were carefully reviewed and selected from 483 submissions. The papers are organized in topical sections on neural networks and their applications, computer vision, image and speech analysis, data mining, hardware implementation, bioinformatics, biometrics and medical applications, concurrent parallel processing, agent systems, robotics and control, artificial intelligence in modeling and simulation, various problems od artificial intelligence.

The Impact of Applications on Mathematics

Masato Wakayama,Robert S. Anderssen,Jin Cheng,Yasuhide Fukumoto,Robert McKibbin,Konrad Polthier,Tsuyoshi Takagi,Kim-Chuan Toh
The Impact of Applications on Mathematics Book PDF

Author : Masato Wakayama,Robert S. Anderssen,Jin Cheng,Yasuhide Fukumoto,Robert McKibbin,Konrad Polthier,Tsuyoshi Takagi,Kim-Chuan Toh
Publisher : Springer
Page : 369 pages
File Size : 46,6 Mb
Release : 2014-07-18
Category : Mathematics
ISBN : 9784431549079

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The Impact of Applications on Mathematics by Masato Wakayama,Robert S. Anderssen,Jin Cheng,Yasuhide Fukumoto,Robert McKibbin,Konrad Polthier,Tsuyoshi Takagi,Kim-Chuan Toh Pdf

This book is a collection of papers presented at the Forum “The Impact of Applications on Mathematics” in October 2013. It describes an appropriate framework in which to highlight how real-world problems, over the centuries and today, have influenced and are influencing the development of mathematics and thereby, how mathematics is reshaped, in order to advance mathematics and its application. The contents of this book address productive and successful interaction between industry and mathematicians, as well as the cross-fertilization and collaboration that result when mathematics is involved with the advancement of science and technology.

Machine Learning and Knowledge Discovery in Databases

Annalisa Appice,Pedro Pereira Rodrigues,Vítor Santos Costa,Carlos Soares,João Gama,Alípio Jorge
Machine Learning and Knowledge Discovery in Databases Book PDF

Author : Annalisa Appice,Pedro Pereira Rodrigues,Vítor Santos Costa,Carlos Soares,João Gama,Alípio Jorge
Publisher : Springer
Page : 709 pages
File Size : 47,5 Mb
Release : 2015-08-28
Category : Computers
ISBN : 9783319235288

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Machine Learning and Knowledge Discovery in Databases by Annalisa Appice,Pedro Pereira Rodrigues,Vítor Santos Costa,Carlos Soares,João Gama,Alípio Jorge Pdf

The three volume set LNAI 9284, 9285, and 9286 constitutes the refereed proceedings of the European Conference on Machine Learning and Knowledge Discovery in Databases, ECML PKDD 2015, held in Porto, Portugal, in September 2015. The 131 papers presented in these proceedings were carefully reviewed and selected from a total of 483 submissions. These include 89 research papers, 11 industrial papers, 14 nectar papers, and 17 demo papers. They were organized in topical sections named: classification, regression and supervised learning; clustering and unsupervised learning; data preprocessing; data streams and online learning; deep learning; distance and metric learning; large scale learning and big data; matrix and tensor analysis; pattern and sequence mining; preference learning and label ranking; probabilistic, statistical, and graphical approaches; rich data; and social and graphs. Part III is structured in industrial track, nectar track, and demo track.

Machine Learning

Sergios Theodoridis
Machine Learning Book PDF

Author : Sergios Theodoridis
Publisher : Academic Press
Page : 1160 pages
File Size : 50,9 Mb
Release : 2020-02-19
Category : Computers
ISBN : 9780128188040

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Machine Learning by Sergios Theodoridis Pdf

Machine Learning: A Bayesian and Optimization Perspective, 2nd edition, gives a unified perspective on machine learning by covering both pillars of supervised learning, namely regression and classification. The book starts with the basics, including mean square, least squares and maximum likelihood methods, ridge regression, Bayesian decision theory classification, logistic regression, and decision trees. It then progresses to more recent techniques, covering sparse modelling methods, learning in reproducing kernel Hilbert spaces and support vector machines, Bayesian inference with a focus on the EM algorithm and its approximate inference variational versions, Monte Carlo methods, probabilistic graphical models focusing on Bayesian networks, hidden Markov models and particle filtering. Dimensionality reduction and latent variables modelling are also considered in depth. This palette of techniques concludes with an extended chapter on neural networks and deep learning architectures. The book also covers the fundamentals of statistical parameter estimation, Wiener and Kalman filtering, convexity and convex optimization, including a chapter on stochastic approximation and the gradient descent family of algorithms, presenting related online learning techniques as well as concepts and algorithmic versions for distributed optimization. Focusing on the physical reasoning behind the mathematics, without sacrificing rigor, all the various methods and techniques are explained in depth, supported by examples and problems, giving an invaluable resource to the student and researcher for understanding and applying machine learning concepts. Most of the chapters include typical case studies and computer exercises, both in MATLAB and Python. The chapters are written to be as self-contained as possible, making the text suitable for different courses: pattern recognition, statistical/adaptive signal processing, statistical/Bayesian learning, as well as courses on sparse modeling, deep learning, and probabilistic graphical models. New to this edition: Complete re-write of the chapter on Neural Networks and Deep Learning to reflect the latest advances since the 1st edition. The chapter, starting from the basic perceptron and feed-forward neural networks concepts, now presents an in depth treatment of deep networks, including recent optimization algorithms, batch normalization, regularization techniques such as the dropout method, convolutional neural networks, recurrent neural networks, attention mechanisms, adversarial examples and training, capsule networks and generative architectures, such as restricted Boltzman machines (RBMs), variational autoencoders and generative adversarial networks (GANs). Expanded treatment of Bayesian learning to include nonparametric Bayesian methods, with a focus on the Chinese restaurant and the Indian buffet processes. Presents the physical reasoning, mathematical modeling and algorithmic implementation of each method Updates on the latest trends, including sparsity, convex analysis and optimization, online distributed algorithms, learning in RKH spaces, Bayesian inference, graphical and hidden Markov models, particle filtering, deep learning, dictionary learning and latent variables modeling Provides case studies on a variety of topics, including protein folding prediction, optical character recognition, text authorship identification, fMRI data analysis, change point detection, hyperspectral image unmixing, target localization, and more

Fixed Points

Stepan Karamardian
Fixed Points Book PDF

Author : Stepan Karamardian
Publisher : Academic Press
Page : 506 pages
File Size : 40,5 Mb
Release : 2014-05-10
Category : Mathematics
ISBN : 9781483261133

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Fixed Points by Stepan Karamardian Pdf

Fixed Points: Algorithms and Applications covers the proceedings of the First International Conference on Computing Fixed Points with Applications, held in the Department of Mathematical Sciences at Clemson University, Clemson, South Carolina on June 26-28, 1974. This book is composed of 21 chapters and starts with reviews of finding roots of polynomials by pivoting procedures and the relations between convergence and labeling in approximation algorithm. The next chapters deal with the principles of complementary pivot theory and the Markovian decision chains; the method of continuation for Brouwer fixed point calculation; a fixed point approach to stability in cooperative games; and computation of fixed points in a nonconvex region. Other chapters discuss a computational comparison of fixed point algorithms, the fundamentals of union jack triangulations, and some aspects of Mann’s iterative method for approximating fixed points. The final chapters consider the application of fixed point algorithms to the analysis of tax policies and the pricing for congestion in telephone networks. This book will prove useful to mathematicians, computer scientists, and advance mathematics students.

Topics in Applied Analysis and Optimisation

Michael Hintermüller,José Francisco Rodrigues
Topics in Applied Analysis and Optimisation Book PDF

Author : Michael Hintermüller,José Francisco Rodrigues
Publisher : Springer Nature
Page : 396 pages
File Size : 46,7 Mb
Release : 2019-11-27
Category : Mathematics
ISBN : 9783030331160

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Topics in Applied Analysis and Optimisation by Michael Hintermüller,José Francisco Rodrigues Pdf

This volume comprises selected, revised papers from the Joint CIM-WIAS Workshop, TAAO 2017, held in Lisbon, Portugal, in December 2017. The workshop brought together experts from research groups at the Weierstrass Institute in Berlin and mathematics centres in Portugal to present and discuss current scientific topics and to promote existing and future collaborations. The papers include the following topics: PDEs with applications to material sciences, thermodynamics and laser dynamics, scientific computing, nonlinear optimization and stochastic analysis.

Optimization for Machine Learning

Suvrit Sra,Sebastian Nowozin,Stephen J. Wright
Optimization for Machine Learning Book PDF

Author : Suvrit Sra,Sebastian Nowozin,Stephen J. Wright
Publisher : MIT Press
Page : 509 pages
File Size : 50,8 Mb
Release : 2012
Category : Computers
ISBN : 9780262016469

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Optimization for Machine Learning by Suvrit Sra,Sebastian Nowozin,Stephen J. Wright Pdf

An up-to-date account of the interplay between optimization and machine learning, accessible to students and researchers in both communities. The interplay between optimization and machine learning is one of the most important developments in modern computational science. Optimization formulations and methods are proving to be vital in designing algorithms to extract essential knowledge from huge volumes of data. Machine learning, however, is not simply a consumer of optimization technology but a rapidly evolving field that is itself generating new optimization ideas. This book captures the state of the art of the interaction between optimization and machine learning in a way that is accessible to researchers in both fields. Optimization approaches have enjoyed prominence in machine learning because of their wide applicability and attractive theoretical properties. The increasing complexity, size, and variety of today's machine learning models call for the reassessment of existing assumptions. This book starts the process of reassessment. It describes the resurgence in novel contexts of established frameworks such as first-order methods, stochastic approximations, convex relaxations, interior-point methods, and proximal methods. It also devotes attention to newer themes such as regularized optimization, robust optimization, gradient and subgradient methods, splitting techniques, and second-order methods. Many of these techniques draw inspiration from other fields, including operations research, theoretical computer science, and subfields of optimization. The book will enrich the ongoing cross-fertilization between the machine learning community and these other fields, and within the broader optimization community.