Wavelets and their use

Abstract

This review paper is intended to give a useful guide for those who want to apply discrete wavelets in their practice. The notion of wavelets and their use in practical computing and various applications are briefly described, but rigorous proofs of mathematical statements are omitted, and the reader is just referred to corresponding literature. The multiresolution analysis and fast wavelet transform became a standard procedure for dealing with discrete wavelets. The proper choice of a wavelet and use of nonstandard matrix multiplication are often crucial for achievement of a goal. Analysis of various functions with the help of wavelets allows to reveal fractal structures, singularities etc. Wavelet transform of operator expressions helps solve some equations. In practical applications one deals often with the discretized functions, and the problem of stability of wavelet transform and corresponding numerical algorithms becomes important. After discussing all these topics we turn to practical applications of the wavelet machinery. They are so numerous that we have to limit ourselves by some examples only. The authors would be grateful for any comments which improve this review paper and move us closer to the goal proclaimed in the first phrase of the abstract.

63 pages with 22 ps-figures, to be published in Physics-Uspekhi

Cited by in corpus (8)

• Quantum-Gravity Analysis of Gamma-Ray Bursts using Wavelets
• Finding morphology points of electrocardiographic signal waves using wavelet analysis
• Study of time lags in HETE-2 Gamma-Ray Bursts with redshift: search for astrophysical effects and Quantum Gravity signature
• Resonance Structure in the $\gamma \gamma$ Invariant Mass Spectrum in $p$C- and $d$C-Interactions
• Wavelet treatment of the intra-chain correlation functions of homopolymers in dilute solutions
• The redshift distribution of absorption-line systems in QSO spectra
• Two-dimensional discrete wavelet analysis of multiparticle event topology in heavy ion collisions
• Wavelets and sparsity for Faraday tomography