DMCA
The Lifting Scheme: A New Philosophy in Biorthogonal Wavelet Constructions (1995)
| Venue: | in Wavelet Applications in Signal and Image Processing III |
| Citations: | 198 - 0 self |
BibTeX
@INPROCEEDINGS{Sweldens95thelifting,
author = {Wim Sweldens},
title = {The Lifting Scheme: A New Philosophy in Biorthogonal Wavelet Constructions},
booktitle = {in Wavelet Applications in Signal and Image Processing III},
year = {1995},
pages = {68--79}
}
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Abstract
In this paper we present the basic idea behind the lifting scheme, a new construction of biorthogonal wavelets which does not use the Fourier transform. In contrast with earlier papers we introduce lifting purely from a wavelet transform point of view and only consider the wavelet basis functions in a later stage. We show how lifting leads to a faster, fully in-place implementation of the wavelet transform. Moreover, it can be used in the construction of second generation wavelets, wavelets that are not necessarily translates and dilates of one function. A typical example of the latter are wavelets on the sphere. Keywords: wavelet, biorthogonal, in-place calculation, lifting 1 Introduction At the present day it has become virtually impossible to give the definition of a "wavelet". The research field is growing so fast and novel contributions are made at such a rate that even if one manages to give a definition today, it might be obsolete tomorrow. One, very vague, way of thinking about...
Keyphrases
biorthogonal wavelet construction new philosophy later stage definition today research field wavelet basis function fourier transform typical example second generation wavelet in-place calculation basic idea novel contribution wavelet transform point present day in-place implementation obsolete tomorrow biorthogonal wavelet new construction wavelet transform
