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   -> Volume 4, Issue 2


Preprint: The lifting scheme: A custom-design wavelet construction
 
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Wim Sweldens (sweldens@math.sc.edu)
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PostPosted: Mon Dec 02, 2002 5:42 pm    
Subject: Preprint: The lifting scheme: A custom-design wavelet construction
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Preprint: The lifting scheme: A custom-design wavelet construction

Title: The Lifting Scheme: A Custom-Design Construction
of Biorthogonal Wavelets
Author: Wim Sweldens

Abstract:

We present the lifting scheme, a new idea of constructing compactly
supported wavelets with compactly supported duals. The lifting scheme
provides a simple relationship between all multiresolution analyses with
the same scaling function. It isolates the degrees of freedom remaining
after fixing the biorthogonality relations. Then one has full control
over these degrees of freedom to custom-design the wavelet for a particular
application. It also leads to a faster implementation of the fast wavelet
transform. We illustrate the use of the lifting scheme in the construction of
wavelets with interpolating scaling functions.

Industrial Mathematics Initiative, University of South Carolina,
Research Report 1994:07, available through anonymous ftp at
ftp://ftp.math.sc.edu/pub/imi_94/imi94_7.ps or imi95_7.ps.gz.
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