Full paper in PDF:
$% W. Freeden, T. Maier, and S. Zimmermann, A survey on wavelet methods for (geo) applications, Rev. Mat. Complut. 16 (2003), 277–310.%$

A Survey on Wavelet Methods for (Geo) Applications

Willi FREEDEN, Thorsten MAIER,
and Steffen ZIMMERMANN
University of Kaiserslautern
Geomathematics Group
D-67653 Kaiserslautern
P.O.Box 3049 — Germany
freeden@mathematik.uni-kl.de

Received: January 29, 2002
Accepted: June 27, 2002
ABSTRACT

Wavelets originated in 1980’s for the analysis of (seismic) signals and have seen an explosion of applications. However, almost all the material is based on wavelets over Euclidean spaces. This paper deals with an approach to the theory and algorithmic aspects of wavelets in a general separable Hilbert space framework. As examples Legendre wavelets on the interval [-1, +1] and scalar and vector spherical wavelets on the unit sphere _O_ are discussed in more detail.

Key words: wavelet theory, scalar multiscale approximation, vectorial multiscale approximation, pyramid scheme, geoapplications.
2000 Mathematics Subject Classification: 65T60, 65Z05, 42C40, 86A25.