Finite Frames

Theory and Applications

  • Peter G. Casazza
  • Gitta Kutyniok

Part of the Applied and Numerical Harmonic Analysis book series (ANHA)

Table of contents

  1. Front Matter
    Pages I-XVI
  2. Peter G. Casazza, Gitta Kutyniok, Friedrich Philipp
    Pages 1-53
  3. Matthew Fickus, Dustin G. Mixon, Miriam J. Poteet
    Pages 55-107
  4. Peter G. Casazza, Darrin Speegle
    Pages 109-139
  5. Jameson Cahill, Nate Strawn
    Pages 141-170
  6. Shayne Waldron
    Pages 171-191
  7. Götz E. Pfander
    Pages 193-239
  8. Bernhard G. Bodmann
    Pages 241-266
  9. Alexander M. Powell, Rayan Saab, Özgür Yılmaz
    Pages 267-302
  10. Waheed U. Bajwa, Ali Pezeshki
    Pages 303-335
  11. Matthew Fickus, Melody L. Massar, Dustin G. Mixon
    Pages 337-379
  12. Martin Ehler, Kasso A. Okoudjou
    Pages 415-436
  13. Peter G. Casazza, Gitta Kutyniok
    Pages 437-477
  14. Back Matter
    Pages 479-485

About this 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.

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 frame decomposition redundancy signal processing sparse representations tight frames

Editors and affiliations

  • Peter G. Casazza
    • 1
  • Gitta Kutyniok
    • 2
  1. 1., Department of MathematicsUniversity of MissouriColumbiaUSA
  2. 2., Institut für MathematikTechnische Universität BerlinBerlinGermany

Bibliographic information