Two-Dimensional Wavelets and their Relatives

Comprehensive treatment of 2-D wavelets for engineers, physicists and mathematicians.

Jean-Pierre Antoine (Author), Romain Murenzi (Author), Pierre Vandergheynst (Author), Syed Twareque Ali (Author)

9780521065191, Cambridge University Press

Paperback / softback, published 12 June 2008

480 pages, 134 b/w illus. 3 tables
24.6 x 18.7 x 2.9 cm, 0.87 kg

Review of the hardback: 'This book is of great interest to anyone working in 2-d CWT and their applications.' Zentralblatt MATH

Two-dimensional wavelets offer a number of advantages over discrete wavelet transforms when processing rapidly varying functions and signals. In particular, they offer benefits for real-time applications such as medical imaging, fluid dynamics, shape recognition, image enhancement and target tracking. This book introduces the reader to 2-D wavelets via 1-D continuous wavelet transforms, and includes a long list of useful applications. The authors then describe in detail the underlying mathematics before moving on to more advanced topics such as matrix geometry of wavelet analysis, three-dimensional wavelets and wavelets on a sphere. Throughout the book, practical applications and illustrative examples are used extensively, ensuring the book's value to engineers, physicists and mathematicians alike.

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.

Subject Areas: Signal processing [UYS], Electronics & communications engineering [TJ], Physics [PH], Applied mathematics [PBW]