Sampling Theory and Wavelets
A Fischer · 1999
Abstract Over the past decade wavelets and wavelet techniques have become increasingly important in the more applied areas of mathematics. There seems to be hardly any field untouched by the recent preoccupation with these and related concepts. Their effectiveness in data compression makes them invaluable for the compression of auditory signals and images (Mallat 1989b; Wickerhauser 1991; Benedetto and Teolis 1993), their usefulness being further enhanced by their suitability for edge detection (Froment and Mallat 1992; Antoine et al. 1993). Wavelet and more general multilevel methods have been shown to be extremely efficient for the preconditioning of linear systems stemming from Galerkin approximations for elliptic problems (Dahmen and Kunoth 1992; Jaffard 1992).