Wavelets

Wavelets: A Tutorial in Theory and Applications is the second volume in the new series WAVELET ANALYSIS AND ITS APPLICATIONS. As a companion to the first volume in this series, this volume covers several of the most important areas in wavelets, ranging from the development of the basic theory such as construction and analysis of wavelet bases to an introduction of some of the key applications, including Mallat's local wavelet maxima technique in second generation image coding. A fairly extensive bibliography is also included in this volume.- Covers several of the most important areas in wavelets, ranging from the development of the basic theory, such as: Construction and analysis of wavelet bases
- Introduction of some of the key applications, including Mallat's local wavelet maxima technique in second generation image coding
- Extensive bibliography is also included in this volume
- Companion to the first volume in this series, An Introduction to Wavelets, and can be used as supplementary instructional material for a two-semester course on wavelet analysis

Preface. Orthogonal Wavelets: D. Pollen, Daubechies' Scaling Function on [0,3]. P.N. Heller, H.L. Resnikoff, and R.O. Wells, Jr., Wavelet Matrices and the Representation of Discrete Functions. G.G. Walter, Wavelets and Generalized Functions. Semi-orthogonal and Nonorthogonal Wavelets: G. Battle, Cardinal Spline Interpolation and the Block Spin Construction of Wavelets. M. Unser and A. Aldroubi, Polynomial Splines and Wavelets--A Signal Processing Perspective. A. Cohen, Biorthogonal Wavelets. J.-C. Feauveau, Nonorthogonal Multiresolution Analysis Using Wavelets. Wavelet-like Local Bases: B.K. Alpert, Wavelets and Other Bases for Fast Numerical Linear Algebra. P. Auscher, Wavelets with Boundary Conditions on the Interval. P. Auscher, G. Weiss, and M.V. Wickerhauser, Local Sine and Cosine Bases of Coifman and Meyer and the Construction of Smooth Wavelets. Multivariate Scaling Functions and Wavelets: W.R. Madych, Some Elementary Properties of Multiresolution Analysis of L2 (Rn). M.A. Berger and Y. Wang, Multi-Dimensional Two-Scale Dilation Equations. J. St*adockler, Multivariate Wavelets. Short-time Fourier and Window-Radon Transforms: H.G. Feichtinger and K. Gr*adochenig, Gabor Wavelets and the Heisenberg Group: Gabor Expansions and Short Time Fourier Transform from the Group Theoretical Point of View. G. Kaiser and R.F. Streater, Windowed Radon Transforms, Analytic Signals, and the Wave Equation. Theory of Sampling and Interpolation: J.J. Benedetto, Irregular Sampling and Frames. A. Aldroubi and M. Unser, Families of Wavelet Transforms in Connection with Shannon's Sampling Theory and the Gabor Transform. K. Seip, Wavelets in H2(R): Sampling, Interpolation, and Phase Space Density. Applications to Numerical Analysis and Signal Processing: S. Jaffard and Ph. Lauren*aycot, Orthonormal Wavelets, Analysis of Operators, and Applications to Numerical Analysis. R.A. Gopinath and C.S. Burrus, Wavelet Transforms and Filter Banks. J. Froment and S. Mallat, Second Generation Compact Image Coding with Wavelets. M.V. Wickerhauser, Acoustic Signal Compression with Wavelet Packets. Bibliography. Subject Index.