"Beyond Wavelets" presents state-of-the-art theories, methods, algorithms, and applications of mathematical extensions for classical wavelet analysis. Wavelets, introduced 20 years ago byMorlet 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 mathematicalfoundations 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 amethod 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.View full description
anyone interested in wavelet technology, including mathematicians, physical scientists, engineers, etc.
- Published: September 2003
- Imprint: ACADEMIC PRESS
- ISBN: 978-0-12-743273-1
"The text is well prepared, and the cast of authors is impressive. If you are a researcher in image processing using wavelets, this book is worth owning." - Robert Lund, Clemson University in the Journal of the American Statistical Association
Table of ContentsPrefaceDigital Ridgelet Transform based Trude Ridge Functions, D.L. Donoho and A.G. Flesia.Digital Implementation of Ridgelet Packets, A.G. Flesia, H. Hel-Or, A. Averbuch, E.J. CandÃ¨s, R.R. Coifman andD.L. Donoho.Brushlets: Steerable Wavelet Packets, F.G. Meyer and R.R. Coifman.Countourlets, M.N. Do and M. Vetterli.ENO-wavelet Tranforms and Some Applications, T.F. Chan and Hao-Min Zhou.A Mechanical Image Model for Bayesian Tomographic Reconstruction, S. Zhao and H.Cai.Sparsity vs. Statistical Independence in Adaptive Signal Representations: A Case Study of the Spike Process, B. BÃ©nichou and N. Saito.Nonuniform Filter Banks: New Results and Open Problems, S. Akkarakaran and P.P. Vaidyanathan.Recent Development of Spline Wavelet Frames with Compact Support, C.K> Chui and J. StÃ¶ckler.Affine, Quasi-Affine and Co-Affine Wavelets, P. Gressman, D. Labate, G. Weiss and E.N. Wilson.Index.