AMS Bookstore LOGO amslogo
Return to List

AMS TextbooksAMS Applications-related Books

Oscillating Patterns in Image Processing and Nonlinear Evolution Equations: The Fifteenth Dean Jacqueline B. Lewis Memorial Lectures
Yves Meyer, École Normale Supérieure de Cachan, France
SEARCH THIS BOOK:

University Lecture Series
2001; 122 pp; softcover
Volume: 22
ISBN-10: 0-8218-2920-3
ISBN-13: 978-0-8218-2920-2
List Price: US$28
Member Price: US$22.40
Order Code: ULECT/22
[Add Item]

Request Permissions

Image compression, the Navier-Stokes equations, and detection of gravitational waves are three seemingly unrelated scientific problems that, remarkably, can be studied from one perspective. The notion that unifies the three problems is that of "oscillating patterns", which are present in many natural images, help to explain nonlinear equations, and are pivotal in studying chirps and frequency-modulated signals.

The first chapter of this book considers image processing, more precisely algorithms of image compression and denoising. This research is motivated in particular by the new standard for compression of still images known as JPEG-2000. The second chapter has new results on the Navier-Stokes and other nonlinear evolution equations. Frequency-modulated signals and their use in the detection of gravitational waves are covered in the final chapter.

In the book, the author describes both what the oscillating patterns are and the mathematics necessary for their analysis. It turns out that this mathematics involves new properties of various Besov-type function spaces and leads to many deep results, including new generalizations of famous Gagliardo-Nirenberg and Poincaré inequalities.

This book is based on the "Dean Jacqueline B. Lewis Memorial Lectures" given by the author at Rutgers University. It can be used either as a textbook in studying applications of wavelets to image processing or as a supplementary resource for studying nonlinear evolution equations or frequency-modulated signals. Most of the material in the book did not appear previously in monograph literature.

Readership

Graduate students and researchers working in functional analysis and its applications, in particular to signal and image processing.

Table of Contents

  • Still images compression
  • The role of oscillations in some nonlinear PDE's
  • Frequency modulated signals, chirps and the Virgo program
  • Conclusion
  • References
Powered by MathJax

  AMS Home | Comments: webmaster@ams.org
© Copyright 2014, American Mathematical Society
Privacy Statement

AMS Social

AMS and Social Media LinkedIn Facebook Podcasts Twitter YouTube RSS Feeds Blogs Wikipedia