The wavelet transform can be seen as a synthesis of ideas that have emerged since the 1960s in mathematics, physics, and electrical engineering. The basic idea is to use a family of 'building blocks' to represent in an efficient way the object at hand, be it a function, an operator, a signal, or an image. The building blocks themselves come in different 'sizes' which can describe different features with different resolutions. The papers in this book attempt to give some theoretical and technical shape to this intuitive picture of wavelets and their uses. The papers collected here were prepared for an AMS Short Course on Wavelets and Applications, held at the Joint Mathematics Meetings in San Antonio in January 1993.Here readers will find general background on wavelets as well as more detailed views of specific techniques and applications. With contributions by some of the top experts in the field, this book provides an excellent introduction to this important and growing area of research.
Wavelet transforms and orthonormal wavelet bases by I. Daubechies Wavelets and operators by Y. Meyer Projection operators in multiresolution analysis by P. G. Lemarie-Rieusset Wavelets and differential operators by P. Tchamitchian Wavelets and fast numerical algorithms by G. Beylkin Wavelets and adapted waveform analysis. A toolkit for signal processing and numerical analysis by R. R. Coifman and M. V. Wickerhauser Best-adapted wavelet packet bases by M. V. Wickerhauser Nonlinear wavelet methods for recovery of signals, densities, and spectra from indirect and noisy data by D. L. Donoho.