Finite Frames - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Finite Frames write by Peter G. Casazza. This book was released on 2012-09-13. Finite Frames available in PDF, EPUB and Kindle. 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 Frames
Finite Frames - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Finite Frames write by Peter G. Casazza. This book was released on 2012-09-14. Finite Frames available in PDF, EPUB and Kindle. 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
Finite Frame Theory: A Complete Introduction to Overcompleteness - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Finite Frame Theory: A Complete Introduction to Overcompleteness write by Kasso A. Okoudjou. This book was released on 2016-07-13. Finite Frame Theory: A Complete Introduction to Overcompleteness available in PDF, EPUB and Kindle. 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.
An Introduction to Finite Tight Frames
An Introduction to Finite Tight Frames - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook An Introduction to Finite Tight Frames write by Shayne F. D. Waldron. This book was released on 2018-02-03. An Introduction to Finite Tight Frames available in PDF, EPUB and Kindle. 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.
An Introduction to Frames and Riesz Bases
An Introduction to Frames and Riesz Bases - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook An Introduction to Frames and Riesz Bases write by Ole Christensen. This book was released on 2016-05-24. An Introduction to Frames and Riesz Bases available in PDF, EPUB and Kindle. 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
