Finite Frames: Theory and Applications

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Peter G. Casazza, Gitta Kutyniok
Springer Science & Business Media, Sep 13, 2012 - Mathematics - 485 pages
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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.

 

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Contents

Introduction to Finite Frame Theory
1
Constructing Finite Frames with a Given Spectrum
54
Spanning and Independence Properties of Finite Frames
109
Algebraic Geometry and Finite Frames
140
Group Frames
171
Gabor Frames in Finite Dimensions
193
Frames as Codes
240
Quantization and Finite Frames
267
Finite Frames for Sparse Signal Processing
303
Finite Frames and Filter Banks
337
The KadisonSinger and Paulsen Problems in Finite Frame Theory
380
Probabilistic Frames An Overview
415
Fusion Frames
437
Index
478
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