Beyond Wavelets

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Grant Welland
Academic Press, Dec 11, 2003 - Mathematics - 320 pages
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"Beyond Wavelets" presents state-of-the-art theories, methods, algorithms, and applications of mathematical extensions for classical wavelet analysis. Wavelets, introduced 20 years ago by
Morlet and Grossmann and developed very rapidly during the 1980's and 1990's, has created a common link between computational mathematics and other disciplines of science and engineering.
Classical wavelets have provided effective and efficient mathematical tools for time-frequency analysis which enhances and replaces the Fourier approach.

However, with the current advances in science and technology, there is an immediate need to extend wavelet mathematical tools as well. "Beyond Wavelets" presents a list of ideas and mathematical
foundations for such extensions, including: continuous and digital ridgelets, brushlets, steerable wavelet packets, contourlets, eno-wavelets, spline-wavelet frames, and quasi-affine wavelets. Wavelet subband algorithms are extended to pyramidal directional and nonuniform filter banks. In addition, this volume includes a
method for tomographic reconstruction using a mechanical image model and a statistical study for independent adaptive signal representation.

Investigators already familiar with wavelet methods from areas such as engineering, statistics, and mathematics will benefit by owning this volume.

*Curvelets, Contourlets, Ridgelets,
*Digital Implementation of Ridgelet Packets
*Steerable Wavelet Packets
*Essentially Non-Oscillatory Wavelets
*Medical Imaging
*Non-Uniform Filter Banks
*Spline-wavelet frames and
*Vanishing Moment Recovery Functions
 

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Contents

Chapter 1 Digital Ridgelet Transform based on True Ridge Functions
1
Chapter 2 Digital Implementation of Ridgelet Packets
31
Steerable Wavelet Packets
61
Chapter 4 Contourlets
83
Chapter 5 ENOwavelet Transforms and Some Applications
107
Chapter 6 A Mechanical Image Model for Bayesian Tomographic Reconstruction
135
Chapter 7 Recent Development of Spline Wavelet Frames with Compact Support
151
Chapter 8 Afiine QuasiAffine and CoAffine Wavelets
215
A Case Study of the Spike Process
225
New Results and Open Problems
259
Index
303
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