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   -> Volume 5, Issue 1

Answer: Help needed in Multiwavelet Transforms (WD 4.12 #19)
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Tim Downie (

PostPosted: Tue Dec 03, 2002 4:15 pm    
Subject: Answer: Help needed in Multiwavelet Transforms (WD 4.12 #19)
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Answer: Help needed in Multiwavelet Transforms (WD 4.12 #19)

You're problem is not the multiple wavelet transform itself, but as
you found, the decomposition is poor if the data has not been
"preprocessed". For example the Disctrete multiple wavelet transform
applied to a constant signal gives nonzero coefficients, if then one
thresholds These small coefficients to zero, and reconstructs, the
resulting function has a high frequency oscillation (or "noise"). If
a suitable "prefilter" is applied to the data before decomposition,
then constant and linear signals will give zero wavelet coefficients,
as required.

The only papers I have seen which address this aspect of multiple
wavelets are Xia et al "On Discrete Multiwavelet transforms" and
Strela et al. "The application of multiwavelet filterbanks to image
processing". I am also researching the subject, and hope to make the
details available soon.

Tim Downie
Research Student
University of Bristol
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