Finite Frame Theory
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Finite Frames
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Author : Peter G. Casazza
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-09-14
Finite Frames written by Peter G. Casazza and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-09-14 with Mathematics categories.
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.
Finite Frame Theory A Complete Introduction To Overcompleteness
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Author : Kasso A. Okoudjou
language : en
Publisher: American Mathematical Soc.
Release Date : 2016-07-13
Finite Frame Theory A Complete Introduction To Overcompleteness written by Kasso A. Okoudjou and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-07-13 with Mathematics categories.
Frames are overcomplete sets of vectors that can be used to stably and faithfully decompose and reconstruct vectors in the underlying vector space. Frame theory stands at the intersection of many areas in mathematics such as functional and harmonic analysis, numerical analysis, matrix theory, numerical linear algebra, algebraic and differential geometry, probability, statistics, and convex geometry. At the same time its applications in engineering, medicine, computer science, and quantum computing are motivating new research problems in applied and pure mathematics. This volume is based on lectures delivered at the 2015 AMS Short Course “Finite Frame Theory: A Complete Introduction to Overcompleteness”, held January 8–9, 2015 in San Antonio, TX. Mostly written in a tutorial style, the seven chapters contained in this volume survey recent advances in the theory and applications of finite frames. In particular, it presents state-of-the-art results on foundational frame problems, and on the analysis and design of various frames, mostly motivated by specific applications. Carefully assembled, the volume quickly introduces the non-expert to the basic tools and techniques of frame theory. It then moves to develop many recent results in the area and presents some important applications. As such, the volume is designed for a diverse audience including researchers in applied and computational harmonic analysis, as well as engineers and graduate students.
A Bridge Between Lie Theory And Frame Theory
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Author : Vignon Oussa
language : en
Publisher: John Wiley & Sons
Release Date : 2025-03-06
A Bridge Between Lie Theory And Frame Theory written by Vignon Oussa and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-03-06 with Mathematics categories.
Comprehensive textbook examining meaningful connections between the subjects of Lie theory, differential geometry, and signal analysis A Bridge Between Lie Theory and Frame Theory serves as a bridge between the areas of Lie theory, differential geometry, and frame theory, illustrating applications in the context of signal analysis with concrete examples and images. The first part of the book gives an in-depth, comprehensive, and self-contained exposition of differential geometry, Lie theory, representation theory, and frame theory. The second part of the book uses the theories established in the early part of the text to characterize a class of representations of Lie groups, which can be discretized to construct frames and other basis-like systems. For instance, Lie groups with frames of translates, sampling, and interpolation spaces on Lie groups are characterized. A Bridge Between Lie Theory and Frame Theory includes discussion on: Novel constructions of frames possessing additional desired features such as boundedness, compact support, continuity, fast decay, and smoothness, motivated by applications in signal analysis Necessary technical tools required to study the discretization problem of representations at a deep level Ongoing dynamic research problems in frame theory, wavelet theory, time frequency analysis, and other related branches of harmonic analysis A Bridge Between Lie Theory and Frame Theory is an essential learning resource for graduate students, applied mathematicians, and scientists who are looking for a rigorous and complete introduction to the covered subjects.
The Use Of Frames In Sampling Theory
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Author : Antonio García García
language : en
Publisher: Springer Nature
Release Date : 2024-07-26
The Use Of Frames In Sampling Theory written by Antonio García García and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-07-26 with Mathematics categories.
This book provides a comprehensive review of regular sampling based on frame theory in a separable Hilbert space. Thus, sampling theory has common features in almost all situations: classical theory, Kramer sampling theory, and finite sampling or sampling Hilbert–Schmidt operators. In addition, the transversality of sampling theory with other mathematical fields appears, in an easy way. The first three chapters of the book can be used as an introduction to sampling theory, while the rest of the chapters are addressed to introduce the interested reader in the research on the topic.
Wavelets Frames And Operator Theory
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Author : Palle E. T. Jørgensen
language : en
Publisher: American Mathematical Soc.
Release Date : 2004
Wavelets Frames And Operator Theory written by Palle E. T. Jørgensen and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Mathematics categories.
Nineteen papers are presented from a special joint session held in conjunction with the American Mathematical Society's 2003 annual meeting in Baltimore, and a National Science Foundation workshop at the University of Maryland. The papers distinguish themselves by often including applications as wel
An Introduction To Finite Tight Frames
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Author : Shayne F. D. Waldron
language : en
Publisher: Springer
Release Date : 2018-02-03
An Introduction To Finite Tight Frames written by Shayne F. D. Waldron and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-02-03 with Mathematics categories.
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.
Sampling Theory A Renaissance
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Author : Götz E. Pfander
language : en
Publisher: Birkhäuser
Release Date : 2015-12-08
Sampling Theory A Renaissance written by Götz E. Pfander and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-12-08 with Mathematics categories.
Reconstructing or approximating objects from seemingly incomplete information is a frequent challenge in mathematics, science, and engineering. A multitude of tools designed to recover hidden information are based on Shannon’s classical sampling theorem, a central pillar of Sampling Theory. The growing need to efficiently obtain precise and tailored digital representations of complex objects and phenomena requires the maturation of available tools in Sampling Theory as well as the development of complementary, novel mathematical theories. Today, research themes such as Compressed Sensing and Frame Theory re-energize the broad area of Sampling Theory. This volume illustrates the renaissance that the area of Sampling Theory is currently experiencing. It touches upon trendsetting areas such as Compressed Sensing, Finite Frames, Parametric Partial Differential Equations, Quantization, Finite Rate of Innovation, System Theory, as well as sampling in Geometry and Algebraic Topology.
Quantum Theory And Symmetries With Lie Theory And Its Applications In Physics Volume 2
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Author : Vladimir Dobrev
language : en
Publisher: Springer
Release Date : 2018-09-30
Quantum Theory And Symmetries With Lie Theory And Its Applications In Physics Volume 2 written by Vladimir Dobrev and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-09-30 with Science categories.
This book is the second volume of the proceedings of the joint conference X. International Symposium “Quantum Theory and Symmetries” (QTS-X) and XII. International Workshop “Lie Theory and Its Applications in Physics” (LT-XII), 19–25 June 2017, Varna, Bulgaria. The QTS series started around the core concept that symmetries underlie all descriptions of quantum systems. It has since evolved into a symposium on the frontiers of theoretical and mathematical physics. The LT series covers the whole field of Lie Theory in its widest sense together with its applications in many facets of physics. As an interface between mathematics and physics the workshop serves as a meeting place for mathematicians and theoretical and mathematical physicists. In the division of the material between the two volumes, the Editor has tried to select for the first and second volumes papers that are more oriented toward mathematics and physics, respectively. However, this division is relative since many papers could have been placed in either volume. The topics covered in this volume represent the most modern trends in the fields of the joint conferences: symmetries in string theories, conformal field theory, holography, gravity theories and cosmology, gauge theories, foundations of quantum theory, nonrelativistic and classical theories.
Frames And Harmonic Analysis
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Author : Yeonhyang Kim
language : en
Publisher: American Mathematical Soc.
Release Date : 2018-04-27
Frames And Harmonic Analysis written by Yeonhyang Kim and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-04-27 with Education categories.
This volume contains the proceedings of the AMS Special Sessions on Frames, Wavelets and Gabor Systems and Frames, Harmonic Analysis, and Operator Theory, held from April 16-17, 2016, at North Dakota State University in Fargo, North Dakota. The papers appearing in this volume cover frame theory and applications in three specific contexts: frame constructions and applications, Fourier and harmonic analysis, and wavelet theory.
Sampling Theory And Applications
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Author : Stephen D. Casey
language : en
Publisher: Springer Nature
Release Date : 2020-05-20
Sampling Theory And Applications written by Stephen D. Casey and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-05-20 with Mathematics categories.
The chapters of this volume are based on talks given at the eleventh international Sampling Theory and Applications conference held in 2015 at American University in Washington, D.C. The papers highlight state-of-the-art advances and trends in sampling theory and related areas of application, such as signal and image processing. Chapters have been written by prominent mathematicians, applied scientists, and engineers with an expertise in sampling theory. Claude Shannon’s 100th birthday is also celebrated, including an introductory essay that highlights Shannon’s profound influence on the field. The topics covered include both theory and applications, such as: • Compressed sensing• Non-uniform and wave sampling• A-to-D conversion• Finite rate of innovation• Time-frequency analysis• Operator theory• Mobile sampling issues Sampling: Theory and Applications is ideal for mathematicians, engineers, and applied scientists working in sampling theory or related areas.