Finite Frames: Theory and Applications (Applied and Numerical Harmonic Analysis)

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. Annotation 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 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."--Publisher's website This Is A Comprehensive, Systematic Study Of Finite Frame Theory And Applications. Coverage Includes Frame Constructions, Group Frames, Fusion Frames, Pseudo-frames, Frames And Algebraic Geometry, And Robustness Against Erasures. Introduction -- Constructing Finite Frames With A Given Spectrum.-spanning And Independence Properties Of Finite.-alegebraic Geometry And Finite Frames -- Group Frames -- Gabor Framses In Finite dimensions -- Frames As Codes -- Quantization And Finite Frames -- Finite Frames For Sparse Signal Processing -- Finite Frames And Filter Banks -- Finite Frame Theory In Pure Mathematics -- Probabilitstic Frames -- Fusion Frames. Peter G. Casazza, Gitta Kutyniok, Editors. Includes Bibliographical References And Index. Front Matter....Pages I-XVI Introduction to Finite Frame Theory....Pages 1-53 Constructing Finite Frames with a Given Spectrum....Pages 55-107 Spanning and Independence Properties of Finite Frames....Pages 109-139 Algebraic Geometry and Finite Frames....Pages 141-170 Group Frames....Pages 171-191 Gabor Frames in Finite Dimensions....Pages 193-239 Frames as Codes....Pages 241-266 Quantization and Finite Frames....Pages 267-302 Finite Frames for Sparse Signal Processing....Pages 303-335 Finite Frames and Filter Banks....Pages 337-379 The Kadison–Singer and Paulsen Problems in Finite Frame Theory....Pages 381-413 Probabilistic Frames: An Overview....Pages 415-436 Fusion Frames....Pages 437-477 Back Matter....Pages 479-485 This is a comprehensive, systematic study of finite frame theory and applications. Coverage includes frame constructions, group frames, fusion frames, pseudo-frames, frames and algebraic geometry, and robustness against erasures-- Source other than Library of Congress Here is a comprehensive, systematic study of finite frame theory and applications. Coverage includes frame constructions, group frames, fusion frames, pseudo-frames, frames and algebraic geometry, and robustness against erasures.