An Introduction To Finite Tight Frames

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An Introduction to Finite Tight Frames

Shayne F. D. Waldron
An Introduction to Finite Tight Frames Book PDF

Author : Shayne F. D. Waldron
Publisher : Springer
Page : 587 pages
File Size : 45,5 Mb
Release : 2018-02-03
Category : Mathematics
ISBN : 9780817648152

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An Introduction to Finite Tight Frames by Shayne F. D. Waldron Pdf

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.

Finite Frame Theory: A Complete Introduction to Overcompleteness

Kasso A. Okoudjou
Finite Frame Theory A Complete Introduction to Overcompleteness Book PDF

Author : Kasso A. Okoudjou
Publisher : American Mathematical Soc.
Page : 241 pages
File Size : 43,6 Mb
Release : 2016-07-13
Category : Approximations and expansions
ISBN : 9781470420192

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Finite Frame Theory: A Complete Introduction to Overcompleteness by Kasso A. Okoudjou Pdf

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.

Finite Frames

Peter G. Casazza,Gitta Kutyniok
Finite Frames Book PDF

Author : Peter G. Casazza,Gitta Kutyniok
Publisher : Springer Science & Business Media
Page : 492 pages
File Size : 40,9 Mb
Release : 2012-09-14
Category : Mathematics
ISBN : 9780817683733

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Finite Frames by Peter G. Casazza,Gitta Kutyniok Pdf

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.

An Introduction to Frames

Jelena Kovacevic,Amina Chebira
An Introduction to Frames Book PDF

Author : Jelena Kovacevic,Amina Chebira
Publisher : Now Publishers Inc
Page : 110 pages
File Size : 42,9 Mb
Release : 2008
Category : Computers
ISBN : 9781601980687

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An Introduction to Frames by Jelena Kovacevic,Amina Chebira Pdf

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.

Finite Frames

Peter G. Casazza,Gitta Kutyniok
Finite Frames Book PDF

Author : Peter G. Casazza,Gitta Kutyniok
Publisher : Springer Science & Business Media
Page : 492 pages
File Size : 51,6 Mb
Release : 2012-09-13
Category : Mathematics
ISBN : 9780817683726

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Finite Frames by Peter G. Casazza,Gitta Kutyniok Pdf

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.

Frames for Undergraduates

Deguang Han
Frames for Undergraduates Book PDF

Author : Deguang Han
Publisher : American Mathematical Soc.
Page : 314 pages
File Size : 52,9 Mb
Release : 2007
Category : Frames (Vector analysis).
ISBN : 9780821842126

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Frames for Undergraduates by Deguang Han Pdf

"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.

An Introduction to Frames and Riesz Bases

Ole Christensen
An Introduction to Frames and Riesz Bases Book PDF

Author : Ole Christensen
Publisher : Birkhäuser
Page : 704 pages
File Size : 45,8 Mb
Release : 2016-05-24
Category : Mathematics
ISBN : 9783319256139

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An Introduction to Frames and Riesz Bases by Ole Christensen Pdf

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

Operator Theory, Functional Analysis and Applications

M. Amélia Bastos,Luís Castro,Alexei Yu. Karlovich
Operator Theory Functional Analysis and Applications Book PDF

Author : M. Amélia Bastos,Luís Castro,Alexei Yu. Karlovich
Publisher : Springer Nature
Page : 654 pages
File Size : 46,6 Mb
Release : 2021-03-31
Category : Mathematics
ISBN : 9783030519452

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Operator Theory, Functional Analysis and Applications by M. Amélia Bastos,Luís Castro,Alexei Yu. Karlovich Pdf

This book presents 30 articles on the topic areas discussed at the 30th “International Workshop on Operator Theory and its Applications”, held in Lisbon in July 2019. The contributions include both expository essays and original research papers reflecting recent advances in the traditional IWOTA areas and emerging adjacent fields, as well as the applications of Operator Theory and Functional Analysis. The topics range from C*–algebras and Banach *–algebras, Sturm-Liouville theory, integrable systems, dilation theory, frame theory, Toeplitz, Hankel, and singular integral operators, to questions from lattice, group and matrix theories, complex analysis, harmonic analysis, and function spaces. Given its scope, the book is chiefly intended for researchers and graduate students in the areas of Operator Theory, Functional Analysis, their applications and adjacent fields.

A Mathematical Introduction to Compressive Sensing

Simon Foucart,Holger Rauhut
A Mathematical Introduction to Compressive Sensing Book PDF

Author : Simon Foucart,Holger Rauhut
Publisher : Springer Science & Business Media
Page : 634 pages
File Size : 55,9 Mb
Release : 2013-08-13
Category : Computers
ISBN : 9780817649487

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A Mathematical Introduction to Compressive Sensing by Simon Foucart,Holger Rauhut Pdf

At the intersection of mathematics, engineering, and computer science sits the thriving field of compressive sensing. Based on the premise that data acquisition and compression can be performed simultaneously, compressive sensing finds applications in imaging, signal processing, and many other domains. In the areas of applied mathematics, electrical engineering, and theoretical computer science, an explosion of research activity has already followed the theoretical results that highlighted the efficiency of the basic principles. The elegant ideas behind these principles are also of independent interest to pure mathematicians. A Mathematical Introduction to Compressive Sensing gives a detailed account of the core theory upon which the field is build. With only moderate prerequisites, it is an excellent textbook for graduate courses in mathematics, engineering, and computer science. It also serves as a reliable resource for practitioners and researchers in these disciplines who want to acquire a careful understanding of the subject. A Mathematical Introduction to Compressive Sensing uses a mathematical perspective to present the core of the theory underlying compressive sensing.

A First Course in the Sporadic SICs

Blake C. Stacey
A First Course in the Sporadic SICs Book PDF

Author : Blake C. Stacey
Publisher : Springer Nature
Page : 119 pages
File Size : 51,6 Mb
Release : 2021-05-31
Category : Science
ISBN : 9783030761042

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A First Course in the Sporadic SICs by Blake C. Stacey Pdf

This book focuses on the Symmetric Informationally Complete quantum measurements (SICs) in dimensions 2 and 3, along with one set of SICs in dimension 8. These objects stand out in ways that have earned them the moniker of "sporadic SICs". By some standards, they are more approachable than the other known SICs, while by others they are simply atypical. The author forays into quantum information theory using them as examples, and the author explores their connections with other exceptional objects like the Leech lattice and integral octonions. The sporadic SICs take readers from the classification of finite simple groups to Bell's theorem and the discovery that "hidden variables" cannot explain away quantum uncertainty. While no one department teaches every subject to which the sporadic SICs pertain, the topic is approachable without too much background knowledge. The book includes exercises suitable for an elective at the graduate or advanced undergraduate level.

Frames and Bases

Ole Christensen
Frames and Bases Book PDF

Author : Ole Christensen
Publisher : Springer Science & Business Media
Page : 326 pages
File Size : 43,7 Mb
Release : 2008-06-05
Category : Mathematics
ISBN : 9780817646783

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Frames and Bases by Ole Christensen Pdf

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.

Adventures in Graph Theory

W. David Joyner,Caroline Grant Melles
Adventures in Graph Theory Book PDF

Author : W. David Joyner,Caroline Grant Melles
Publisher : Birkhäuser
Page : 327 pages
File Size : 43,8 Mb
Release : 2017-12-28
Category : Mathematics
ISBN : 9783319683836

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Adventures in Graph Theory by W. David Joyner,Caroline Grant Melles Pdf

This textbook acts as a pathway to higher mathematics by seeking and illuminating the connections between graph theory and diverse fields of mathematics, such as calculus on manifolds, group theory, algebraic curves, Fourier analysis, cryptography and other areas of combinatorics. An overview of graph theory definitions and polynomial invariants for graphs prepares the reader for the subsequent dive into the applications of graph theory. To pique the reader’s interest in areas of possible exploration, recent results in mathematics appear throughout the book, accompanied with examples of related graphs, how they arise, and what their valuable uses are. The consequences of graph theory covered by the authors are complicated and far-reaching, so topics are always exhibited in a user-friendly manner with copious graphs, exercises, and Sage code for the computation of equations. Samples of the book’s source code can be found at github.com/springer-math/adventures-in-graph-theory. The text is geared towards advanced undergraduate and graduate students and is particularly useful for those trying to decide what type of problem to tackle for their dissertation. This book can also serve as a reference for anyone interested in exploring how they can apply graph theory to other parts of mathematics.

Linear Algebra for Data Science, Machine Learning, and Signal Processing

Jeffrey A. Fessler,Raj Rao Nadakuditi
Linear Algebra for Data Science Machine Learning and Signal Processing Book PDF

Author : Jeffrey A. Fessler,Raj Rao Nadakuditi
Publisher : Cambridge University Press
Page : 453 pages
File Size : 51,5 Mb
Release : 2024-04-30
Category : Computers
ISBN : 9781009418140

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Linear Algebra for Data Science, Machine Learning, and Signal Processing by Jeffrey A. Fessler,Raj Rao Nadakuditi Pdf

Master matrix methods via engaging data-driven applications, aided by classroom-tested quizzes, homework exercises and online Julia demos.

The XFT Quadrature in Discrete Fourier Analysis

Rafael G. Campos
The XFT Quadrature in Discrete Fourier Analysis Book PDF

Author : Rafael G. Campos
Publisher : Springer
Page : 235 pages
File Size : 50,9 Mb
Release : 2019-05-24
Category : Mathematics
ISBN : 9783030134235

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The XFT Quadrature in Discrete Fourier Analysis by Rafael G. Campos Pdf

This book has two main objectives, the first of which is to extend the power of numerical Fourier analysis and to show by means of theoretical examples and numerous concrete applications that when computing discrete Fourier transforms of periodic and non periodic functions, the usual kernel matrix of the Fourier transform, the discrete Fourier transform (DFT), should be replaced by another kernel matrix, the eXtended Fourier transform (XFT), since the XFT matrix appears as a convergent quadrature of a more general transform, the fractional Fourier transform. In turn, the book’s second goal is to present the XFT matrix as a finite-dimensional transformation that links certain discrete operators in the same way that the corresponding continuous operators are related by the Fourier transform, and to show that the XFT matrix accordingly generates sequences of matrix operators that represent continuum operators, and which allow these operators to be studied from another perspective.

Framelets and Wavelets

Bin Han
Framelets and Wavelets Book PDF

Author : Bin Han
Publisher : Springer
Page : 750 pages
File Size : 53,7 Mb
Release : 2018-01-04
Category : Mathematics
ISBN : 9783319685304

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Framelets and Wavelets by Bin Han Pdf

Marking a distinct departure from the perspectives of frame theory and discrete transforms, this book provides a comprehensive mathematical and algorithmic introduction to wavelet theory. As such, it can be used as either a textbook or reference guide. As a textbook for graduate mathematics students and beginning researchers, it offers detailed information on the basic theory of framelets and wavelets, complemented by self-contained elementary proofs, illustrative examples/figures, and supplementary exercises. Further, as an advanced reference guide for experienced researchers and practitioners in mathematics, physics, and engineering, the book addresses in detail a wide range of basic and advanced topics (such as multiwavelets/multiframelets in Sobolev spaces and directional framelets) in wavelet theory, together with systematic mathematical analysis, concrete algorithms, and recent developments in and applications of framelets and wavelets. Lastly, the book can also be used to teach on or study selected special topics in approximation theory, Fourier analysis, applied harmonic analysis, functional analysis, and wavelet-based signal/image processing.