Two-Dimensional Wavelets and their Relatives

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

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.

Two-dimensional wavelets offer a number of advantages over discrete wavelet transforms, in particular for analysis of real-time signals. This book provides thorough and comprehensive treatment of 2-D wavelets, with extensive use of practical applications and illustrative examples throughout. For engineers, physicists and mathematicians.

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.