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Two-Dimensional Wavelets and their Relatives


  • Date Published: June 2008
  • availability: Available
  • format: Paperback
  • isbn: 9780521065191

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About the Authors
  • 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.

    • The first of its kind in print dealing with the two - and higher - dimensional continuous wavelet transforms, with extensive examples of applications
    • Gradual introduction of the underlying mathematical tools, with very few prerequisites, yet leading the reader to the research frontier
    • Covers both the continuous and the discrete wavelet transforms
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    Reviews & endorsements

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

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    Product details

    • Date Published: June 2008
    • format: Paperback
    • isbn: 9780521065191
    • length: 480 pages
    • dimensions: 246 x 187 x 29 mm
    • weight: 0.87kg
    • contains: 134 b/w illus. 3 tables
    • availability: Available
  • Table of Contents

    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
    Appendix 1

  • Authors

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

    Romain Murenzi, Clark Atlanta University, Georgia
    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, Swiss Federal Institute of Technology, Zürich
    Pierre Vandergheynst is a Professor at the Signal Processing Institute, Swiss Federal Insitute of Technology, Lausanne.

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

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