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   -> Volume 5, Issue 9

Preprint: Factoring Wavelet Transforms into Lifting Steps
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Ingrid Daubechies (

PostPosted: Mon Oct 14, 1996 8:39 pm    
Subject: Preprint: Factoring Wavelet Transforms into Lifting Steps
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#3 Preprint: Factoring Wavelet Transforms into Lifting Steps

Title: Factoring Wavelet Transforms into Lifting Steps

Authors: Ingrid Daubechies and Wim Sweldens

Abstract: The lifting scheme is a new flexible tool for constructing
wavelets and wavelet transforms. In this paper, we use the Euclidean
algorithm to show how any discrete wavelet transform or two band
subband transform with finite filters can be obtained with a finite
number of lifting steps starting from the Lazy wavelet (or polyphase
transform). We show a bound on the number of lifting steps which is
proportional to the length of the filters. This factorization provides
an alternative for the lattice factorization, with the advantage that
it can also be used in the biorthogonal (non-unitary) case. The
lifting factorization asymptotically reduces the computational
complexity of the transform by a factor of two and allows for wavelet
transforms that map integers to integers.

Status: Preprint, Bell Laboratories, Lucent Technologies, 1996.

You can download a copy of this paper from the Web at: (PostScript) (Compressed PostScript)

Ingrid C. Daubechies
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