Beyond Wavelets

9780127432731

0127432736

"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.