An Overview of Wavelet Based Multiresolution Analyses

In this paper an overview of wavelet based multiresolution analyses is presented. First, the continuous wavelet transform in its simplest form is discussed. Then, the definition of a multiresolution analysis is given and how wavelets fit into it is shown. The authors take a closer look at orthogonal...

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Bibliographic Details
Published in:SIAM review 1994-09, Vol.36 (3), p.377-412
Main Authors: Jawerth, Bjο̈rn, Sweldens, Wim
Format: Article
Language:English
Subjects:
Abstract harmonic analysis
Applied mathematics
Approximation
Coefficients
Data compression
Exact sciences and technology
Fourier analysis
Fourier transformations
Image compression
Mathematical analysis
Mathematical functions
Mathematics
Orthogonality
Polynomials
Sciences and techniques of general use
Wavelet analysis
Wavelet transforms
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Summary:In this paper an overview of wavelet based multiresolution analyses is presented. First, the continuous wavelet transform in its simplest form is discussed. Then, the definition of a multiresolution analysis is given and how wavelets fit into it is shown. The authors take a closer look at orthogonal, biorthogonal and semiorthogonal wavelets. The fast wavelet transform, wavelets on an interval, multidimensional wavelets and wavelet packets are discussed. Several examples of wavelet families are introduced and compared. Finally, the essentials of two major applications are outlined: data compression and compression of linear operators.
ISSN:0036-1445
1095-7200
DOI:10.1137/1036095