Wavelets

The term "wavelets" is fairly recent, dating back to the early 1980s, but their origins are much older. They can also be traced to concepts in many different disciplines. In mathematics, these roots include for instance Haar's 1910 paper on what we now call the Haar basis, Calderon's work in 1964 using the reproducing formula and the development of atomic decompositions in harmonic analysis. The deep mathematical properties of wavelets can all be linked to this earlier rich development in pure mathematics. There are many connections of wavelets with yet other fields - the use of scaling in renormalization group techniques in statistical physics, or "refinement" techniques in approximation theory and computer aided design, to name but two. Applications of wavelets range as widely as their roots are diverse; they include simulation, solving PDE's, compression of many types of signal (acoustic, images, medical data), the design of new signal types, the characterization of functions as well as data, automatic smoothing algorithms which smooth "intelligently" and even new theorems in pure mathematics.
Because of the multidisciplinary origins of wavelets, and because of the wide range of their applications, the literature on wavelets tends to be scattered among many different fields, making at least some of it difficult to find or access for many of us. This volume is a compilation of papers connected with the many roots of wavelets, published before 1983. It is the first of two volumes of wavelet reprint papers. The second volume, to be published by SIAM, will cover the next generation of wavelet papers, from about 1983 on. The objective of these volumes is to provide a quick reference for anybody interested in wavelets.