Two-Dimensional Wavelets and their Relatives

by Jean-Pierre Antoine, Romain Murenzi, Pierre Vandergheynst, Syed Twareque Ali

Overview

This book introduces 2-D wavelets via 1-D continuous wavelet transforms. The authors then describe the underlying mathematics before progressing to more advanced topics such as matrix geometry of wavelet analysis and three-dimensional wavelets. Practical applications and illustrative examples are employed extensively throughout, ensuring the book's value to engineers, physicists and mathematicians. Two-dimensional wavelets offer a number of advantages over discrete wavelet transforms, in particular, for analysis of real-time signals in such areas as medical imaging, fluid dynamics, shape recognition, image enhancement and target tracking.

Product Details

ISBN-13:	9780521065191
Publisher:	Cambridge University Press
Publication date:	06/12/2008
Edition description:	New Edition
Pages:	480
Product dimensions:	7.36(w) x 9.69(h) x 1.14(d)

About the Author

Jean-Pierre Antoine is the Professor of Mathematical Physics at the Institut de Physique Théorique, Université catholique de Louvain.

Romain Murenzi is currently Minister of Education, Science, Technology, and Scientific Research of the Republic of Rwanda, on leave of absence from the Department of Physics, Clark Atlanta University, Atlanta, Georgia.

Pierre Vandergheynst is a Professor at the Signal Processing Institute, Swiss Federal Insitute of Technology, Lausanne.

Syed Twareque Ali is a Professor at the Department of Mathematics and Statistics, Concordia University, Montréal.

Table of Contents

Prologue; 1. Warm-up: the 1-D continuous wavelet transform; 2. The 2-D continuous wavelet transform; 3. Some 2-D wavelets and their performances; 4. Applications of the 2-D CWT I. Image processing; 5. Applications of the 2-D CWT II. Physical applications; 6. Matrix geometry of wavelet analysis I; 7. Matrix geometry of wavelet analysis II; 8. Minimal uncertainty and Wigner transformations; 9. Higher-dimensional wavelets; 10. Spatio-temporal wavelets and motion estimation; 11. Beyond wavelets; Epilogue; Appendix 1; Bibliography; Index.

Editorial Reviews

"This authoritative, beautiful book earns a place on any wavelets short list. Highly recommended." CHOICE

"[The book] takes the reader on a journey starting from a heuristic approach to wavelets to the state of the art. The presentation is rigorous, yet easy to follow. I highly recommend this book to both beginners and experts." Mathematical Reviews, Ahmed I. Zayed

From the Publisher