Wavelets and the Lifting Scheme: a 5 Minute Tour
نویسنده
چکیده
The purpose of this paper is to give a very short, \nuts and bolts", introduction to the lifting scheme and provide references for further reading. The lifting scheme is a new method for constructing biorthogonal wavelets. The main di erence with classical constructions [1-3] is that it does not rely on the Fourier transform. This way lifting can be used to construct second generation wavelets, wavelets which are not necessarily translates and dilates of one function. The latter we refer to as rst generation wavelets.
منابع مشابه
The Lifting Scheme: a Construction of Second Generation Wavelets
We present the lifting scheme, a simple construction of second generation wavelets; these are wavelets that are not necessarily translates and dilates of one fixed function. Such wavelets can be adapted to intervals, domains, surfaces, weights, and irregular samples. We show how the lifting scheme leads to a faster, in-place calculation of the wavelet transform. Several examples are included.
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Due to its good decorrelating properties, the wavelet transform is a powerful tool for signal analysis. The lifting scheme is an efficient algorithm to calculate wavelet transforms and it allows for the construction of second-generation wavelets. Furthermore it can easily be converted to an integer transform, which is of great importance for multimedia applications. We show how the lifting sche...
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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 wavel...
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