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Frames And Operator Theory In Analysis And Signal Processing
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Book Synopsis Frames and Operator Theory in Analysis and Signal Processing by : David R. Larson
Download or read book Frames and Operator Theory in Analysis and Signal Processing written by David R. Larson and published by American Mathematical Soc.. This book was released on 2008 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains articles based on talks presented at the Special Session Frames and Operator Theory in Analysis and Signal Processing, held in San Antonio, Texas, in January of 2006.
Download or read book Finite Frames written by Peter G. Casazza and published by Springer Science & Business Media. This book was released on 2012-09-14 with total page 492 pages. Available in PDF, EPUB and Kindle. Book excerpt: Hilbert space frames have long served as a valuable tool for signal and image processing due to their resilience to additive noise, quantization, and erasures, as well as their ability to capture valuable signal characteristics. More recently, finite frame theory has grown into an important research topic in its own right, with a myriad of applications to pure and applied mathematics, engineering, computer science, and other areas. The number of research publications, conferences, and workshops on this topic has increased dramatically over the past few years, but no survey paper or monograph has yet appeared on the subject. Edited by two of the leading experts in the field, Finite Frames aims to fill this void in the literature by providing a comprehensive, systematic study of finite frame theory and applications. With carefully selected contributions written by highly experienced researchers, it covers topics including: * Finite Frame Constructions; * Optimal Erasure Resilient Frames; * Quantization of Finite Frames; * Finite Frames and Compressed Sensing; * Group and Gabor Frames; * Fusion Frames. Despite the variety of its chapters' source and content, the book's notation and terminology are unified throughout and provide a definitive picture of the current state of frame theory. With a broad range of applications and a clear, full presentation, this book is a highly valuable resource for graduate students and researchers across disciplines such as applied harmonic analysis, electrical engineering, quantum computing, medicine, and more. It is designed to be used as a supplemental textbook, self-study guide, or reference book.
Book Synopsis Frames and Bases by : Ole Christensen
Download or read book Frames and Bases written by Ole Christensen and published by Springer Science & Business Media. This book was released on 2008-06-05 with total page 326 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on a streamlined presentation of the author’s successful work, An Introduction to Frames and Riesz Bases, this book develops frame theory as part of a dialogue between mathematicians and engineers. Newly added sections on applications will help mathematically oriented readers to see where frames are used in practice and engineers to discover the mathematical background for applications in their field. The book presents basic results in an accessible way and includes extensive exercises.
Book Synopsis An Introduction to Frames and Riesz Bases by : Ole Christensen
Download or read book An Introduction to Frames and Riesz Bases written by Ole Christensen and published by Birkhäuser. This book was released on 2016-05-24 with total page 719 pages. Available in PDF, EPUB and Kindle. Book excerpt: This revised and expanded monograph presents the general theory for frames and Riesz bases in Hilbert spaces as well as its concrete realizations within Gabor analysis, wavelet analysis, and generalized shift-invariant systems. Compared with the first edition, more emphasis is put on explicit constructions with attractive properties. Based on the exiting development of frame theory over the last decade, this second edition now includes new sections on the rapidly growing fields of LCA groups, generalized shift-invariant systems, duality theory for as well Gabor frames as wavelet frames, and open problems in the field. Key features include: *Elementary introduction to frame theory in finite-dimensional spaces * Basic results presented in an accessible way for both pure and applied mathematicians * Extensive exercises make the work suitable as a textbook for use in graduate courses * Full proofs includ ed in introductory chapters; only basic knowledge of functional analysis required * Explicit constructions of frames and dual pairs of frames, with applications and connections to time-frequency analysis, wavelets, and generalized shift-invariant systems * Discussion of frames on LCA groups and the concrete realizations in terms of Gabor systems on the elementary groups; connections to sampling theory * Selected research topics presented with recommendations for more advanced topics and further readin g * Open problems to stimulate further research An Introduction to Frames and Riesz Bases will be of interest to graduate students and researchers working in pure and applied mathematics, mathematical physics, and engineering. Professionals working in digital signal processing who wish to understand the theory behind many modern signal processing tools may also find this book a useful self-study reference. Review of the first edition: "Ole Christensen’s An Introduction to Frames and Riesz Bases is a first-rate introduction to the field ... . The book provides an excellent exposition of these topics. The material is broad enough to pique the interest of many readers, the included exercises supply some interesting challenges, and the coverage provides enough background for those new to the subject to begin conducting original research." — Eric S. Weber, American Mathematical Monthly, Vol. 112, February, 2005
Book Synopsis An Introduction to Frames by : Jelena Kovacevic
Download or read book An Introduction to Frames written by Jelena Kovacevic and published by Now Publishers Inc. This book was released on 2008 with total page 110 pages. Available in PDF, EPUB and Kindle. Book excerpt: An Introduction to Frames is an introduction to redundant signal representations called frames. These representations have recently emerged as yet another powerful tool in the signal processing toolbox, spurred by a host of recent applications requiring some level of redundancy. It asks the question: Why and where should one use frames? And answers emphatically: Anywhere where redundancy is a must. It then goes on to discuss a host of applications that richly illustrate that answer. An Introduction to Frames is geared primarily toward engineering students and those without extensive mathematical training. It is also intended to help researchers and practitioners decide whether frames are the right tool for their application.
Book Synopsis Gabor And Wavelet Frames by : Zuowei Shen
Download or read book Gabor And Wavelet Frames written by Zuowei Shen and published by World Scientific. This book was released on 2007-08-13 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: Gabor and wavelet analyses have found widespread applications in signal analysis, image processing and many other information-related areas. Both deliver representations that are simultaneously local in time and in frequency. Due to their significance and success in practical applications, they formed some of the core topics of the program “Mathematics and Computation in Imaging Science and Information Processing”, which was held at the Institute for Mathematical Sciences, National University of Singapore, from July to December 2003 and in August 2004. As part of the program, tutorial lectures were conducted by international experts, and they covered a wide spectrum of topics in mathematical image, signal and information processing.This volume includes exposition articles by the tutorial speakers on the foundations of Gabor analysis, subband filters and wavelet algorithms, and operator-theoretic interpolation of wavelets and frames. It also presents research papers on Gabor analysis, written by specialists in their respective areas. The volume takes graduate students and researchers new to the field on a valuable learning journey from introductory Gabor and wavelet analyses to advanced topics of current research.
Book Synopsis Frames for Undergraduates by : Deguang Han
Download or read book Frames for Undergraduates written by Deguang Han and published by American Mathematical Soc.. This book was released on 2007 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: "The early chapters contain the topics from linear algebra that students need to know in order to read the rest of the book. The later chapters are devoted to advanced topics, which allow students with more experience to study more intricate types of frames. Toward that end, a Student Presentation section gives detailed proofs of fairly technical results with the intention that a student could work out these proofs independently and prepare a presentation to a class or research group. The authors have also presented some stories in the Anecdotes section about how this material has motivated and influenced their students."--BOOK JACKET.
Book Synopsis An Operator Perspective on Signals and Systems by : Arthur Frazho
Download or read book An Operator Perspective on Signals and Systems written by Arthur Frazho and published by Springer Science & Business Media. This book was released on 2009-12-29 with total page 430 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this monograph, we combine operator techniques with state space methods to solve factorization, spectral estimation, and interpolation problems arising in control and signal processing. We present both the theory and algorithms with some Matlab code to solve these problems. A classical approach to spectral factorization problems in control theory is based on Riccati equations arising in linear quadratic control theory and Kalman ?ltering. One advantage of this approach is that it readily leads to algorithms in the non-degenerate case. On the other hand, this approach does not easily generalize to the nonrational case, and it is not always transparent where the Riccati equations are coming from. Operator theory has developed some elegant methods to prove the existence of a solution to some of these factorization and spectral estimation problems in a very general setting. However, these techniques are in general not used to develop computational algorithms. In this monograph, we will use operator theory with state space methods to derive computational methods to solve factorization, sp- tral estimation, and interpolation problems. It is emphasized that our approach is geometric and the algorithms are obtained as a special application of the theory. We will present two methods for spectral factorization. One method derives al- rithms based on ?nite sections of a certain Toeplitz matrix. The other approach uses operator theory to develop the Riccati factorization method. Finally, we use isometric extension techniques to solve some interpolation problems.
Author :Palle E. T. Jorgensen Publisher :Springer Science & Business Media ISBN 13 :0817646833 Total Pages :343 pages Book Rating :4.8/5 (176 download)
Book Synopsis Representations, Wavelets, and Frames by : Palle E. T. Jorgensen
Download or read book Representations, Wavelets, and Frames written by Palle E. T. Jorgensen and published by Springer Science & Business Media. This book was released on 2008-08-29 with total page 343 pages. Available in PDF, EPUB and Kindle. Book excerpt: The work of Lawrence Baggett has had a profound impact on the field of abstract harmonic analysis and the many areas of mathematics that use its techniques. His sphere of influence ranges from purely theoretical results regarding the representations of locally compact groups to recent applications of wavelets and frames to problems in sampling theory and image compression. Contributions in this volume reflect this broad scope, and Baggett’s unusual ability to bring together techniques from disparate fields. Recent applications to problems in sampling theory and image compression are included.
Book Synopsis Foundations of Signal Processing by : Martin Vetterli
Download or read book Foundations of Signal Processing written by Martin Vetterli and published by Cambridge University Press. This book was released on 2014-09-04 with total page 745 pages. Available in PDF, EPUB and Kindle. Book excerpt: This comprehensive and engaging textbook introduces the basic principles and techniques of signal processing, from the fundamental ideas of signals and systems theory to real-world applications. Students are introduced to the powerful foundations of modern signal processing, including the basic geometry of Hilbert space, the mathematics of Fourier transforms, and essentials of sampling, interpolation, approximation and compression The authors discuss real-world issues and hurdles to using these tools, and ways of adapting them to overcome problems of finiteness and localization, the limitations of uncertainty, and computational costs. It includes over 160 homework problems and over 220 worked examples, specifically designed to test and expand students' understanding of the fundamentals of signal processing, and is accompanied by extensive online materials designed to aid learning, including Mathematica® resources and interactive demonstrations.
Book Synopsis Wavelet Analysis and Applications by : Tao Qian
Download or read book Wavelet Analysis and Applications written by Tao Qian and published by Springer Science & Business Media. This book was released on 2007-02-24 with total page 567 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume reflects the latest developments in the area of wavelet analysis and its applications. Since the cornerstone lecture of Yves Meyer presented at the ICM 1990 in Kyoto, to some extent, wavelet analysis has often been said to be mainly an applied area. However, a significant percentage of contributions now are connected to theoretical mathematical areas, and the concept of wavelets continuously stretches across various disciplines of mathematics. Key topics: Approximation and Fourier Analysis Construction of Wavelets and Frame Theory Fractal and Multifractal Theory Wavelets in Numerical Analysis Time-Frequency Analysis Adaptive Representation of Nonlinear and Non-stationary Signals Applications, particularly in image processing Through the broad spectrum, ranging from pure and applied mathematics to real applications, the book will be most useful for researchers, engineers and developers alike.
Download or read book Finite Frames written by Peter G. Casazza and published by Springer Science & Business Media. This book was released on 2012-09-13 with total page 492 pages. Available in PDF, EPUB and Kindle. Book excerpt: Hilbert space frames have long served as a valuable tool for signal and image processing due to their resilience to additive noise, quantization, and erasures, as well as their ability to capture valuable signal characteristics. More recently, finite frame theory has grown into an important research topic in its own right, with a myriad of applications to pure and applied mathematics, engineering, computer science, and other areas. The number of research publications, conferences, and workshops on this topic has increased dramatically over the past few years, but no survey paper or monograph has yet appeared on the subject. Edited by two of the leading experts in the field, Finite Frames aims to fill this void in the literature by providing a comprehensive, systematic study of finite frame theory and applications. With carefully selected contributions written by highly experienced researchers, it covers topics including: * Finite Frame Constructions; * Optimal Erasure Resilient Frames; * Quantization of Finite Frames; * Finite Frames and Compressed Sensing; * Group and Gabor Frames; * Fusion Frames. Despite the variety of its chapters' source and content, the book's notation and terminology are unified throughout and provide a definitive picture of the current state of frame theory. With a broad range of applications and a clear, full presentation, this book is a highly valuable resource for graduate students and researchers across disciplines such as applied harmonic analysis, electrical engineering, quantum computing, medicine, and more. It is designed to be used as a supplemental textbook, self-study guide, or reference book.
Book Synopsis An Introduction to Finite Tight Frames by : Shayne F. D. Waldron
Download or read book An Introduction to Finite Tight Frames written by Shayne F. D. Waldron and published by Springer. This book was released on 2018-02-03 with total page 590 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook is an introduction to the theory and applications of finite tight frames, an area that has developed rapidly in the last decade. Stimulating much of this growth are the applications of finite frames to diverse fields such as signal processing, quantum information theory, multivariate orthogonal polynomials, and remote sensing. Featuring exercises and MATLAB examples in each chapter, the book is well suited as a textbook for a graduate course or seminar involving finite frames. The self-contained, user-friendly presentation also makes the work useful as a self-study resource or reference for graduate students, instructors, researchers, and practitioners in pure and applied mathematics, engineering, mathematical physics, and signal processing.
Book Synopsis Computational Signal Processing with Wavelets by : Anthony Teolis
Download or read book Computational Signal Processing with Wavelets written by Anthony Teolis and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: Overview For over a decade now, wavelets have been and continue to be an evolving subject of intense interest. Their allure in signal processing is due to many factors, not the least of which is that they offer an intuitively satisfying view of signals as being composed of little pieces of wa'ues. Making this concept mathematically precise has resulted in a deep and sophisticated wavelet theory that has seemingly limitless applications. This book and its supplementary hands-on electronic: component are meant to appeal to both students and professionals. Mathematics and en gineering students at the undergraduate and graduate levels will benefit greatly from the introductory treatment of the subject. Professionals and advanced students will find the overcomplete approach to signal represen tation and processing of great value. In all cases the electronic component of the proposed work greatly enhances its appeal by providing interactive numerical illustrations. A main goal is to provide a bridge between the theory and practice of wavelet-based signal processing. Intended to give the reader a balanced look at the subject, this book emphasizes both theoretical and practical issues of wavelet processing. A great deal of exposition is given in the beginning chapters and is meant to give the reader a firm understanding of the basics of the discrete and continuous wavelet transforms and their relationship. Later chapters promote the idea that overcomplete systems of wavelets are a rich and largely unexplored area that have demonstrable benefits to offer in many applications.
Book Synopsis Frames in Hilbert C*-modules by : Wu Jing
Download or read book Frames in Hilbert C*-modules written by Wu Jing and published by . This book was released on 2006 with total page 101 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the discovery in the early 1950's, frames have emerged as an important tool in signal processing, image processing, data compression and sampling theory etc. Today, powerful tools from operator theory and Banach space theory are being introduced to the study of frames producing deep results in frame theory.
Book Synopsis Wavelets and Multiscale Analysis by : Jonathan Cohen
Download or read book Wavelets and Multiscale Analysis written by Jonathan Cohen and published by Springer Science & Business Media. This book was released on 2011-03-01 with total page 345 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since its emergence as an important research area in the early 1980s, the topic of wavelets has undergone tremendous development on both theoretical and applied fronts. Myriad research and survey papers and monographs have been published on the subject, documenting different areas of applications such as sound and image processing, denoising, data compression, tomography, and medical imaging. The study of wavelets remains a very active field of research, and many of its central techniques and ideas have evolved into new and promising research areas. This volume, a collection of invited contributions developed from talks at an international conference on wavelets, is divided into three parts: Part I is devoted to the mathematical theory of wavelets and features several papers on wavelet sets and the construction of wavelet bases in different settings. Part II looks at the use of multiscale harmonic analysis for understanding the geometry of large data sets and extracting information from them. Part III focuses on applications of wavelet theory to the study of several real-world problems. Overall, the book is an excellent reference for graduate students, researchers, and practitioners in theoretical and applied mathematics, or in engineering.
Book Synopsis Wavelet Theory and Its Applications by : Randy K. Young
Download or read book Wavelet Theory and Its Applications written by Randy K. Young and published by Springer Science & Business Media. This book was released on 1992-09-30 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: The continuous wavelet transform has deep mathematical roots in the work of Alberto P. Calderon. His seminal paper on complex method of interpolation and intermediate spaces provided the main tool for describing function spaces and their approximation properties. The Calderon identities allow one to give integral representations of many natural operators by using simple pieces of such operators, which are more suited for analysis. These pieces, which are essentially spectral projections, can be chosen in clever ways and have proved to be of tremendous utility in various problems of numerical analysis, multidimensional signal processing, video data compression, and reconstruction of high resolution images and high quality speech. A proliferation of research papers and a couple of books, written in English (there is an earlier book written in French), have emerged on the subject. These books, so far, are written by specialists for specialists, with a heavy mathematical flavor, which is characteristic of the Calderon-Zygmund theory and related research of Duffin-Schaeffer, Daubechies, Grossman, Meyer, Morlet, Chui, and others. Randy Young's monograph is geared more towards practitioners and even non-specialists, who want and, probably, should be cognizant of the exciting proven as well as potential benefits which have either already emerged or are likely to emerge from wavelet theory.
