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   -> Volume 6, Issue 1


Preprint: Thresholding Multiwavelets
 
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Tim Downie (tim.downie@bristol.ac.uk)
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PostPosted: Thu Dec 12, 1996 12:51 pm    
Subject: Preprint: Thresholding Multiwavelets
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#1 Preprint: Thresholding Multiwavelets

Title: The Discrete Multiple Wavelet Transform
and Thresholding Methods

Authors: T.R.Downie & B.W.Silverman

Abstract: Orthogonal wavelet bases have recently been developed using
multiple mother wavelet functions. Applying the discrete multiple
wavelet transform requires the input data to be preprocessed to obtain
a more economical decomposition. We discuss the properties of
several preprocessing methods and their effect on the thresholding
results. We propose a multivariate thresholding method for
multiwavelets where each wavelet coefficient vector is thresholded as
opposed to each element. A multiwavelet universal threshold is
obtained using the asymptotic behaviour of the $chi ^2$
distribution. A simulation study demonstrates that when using the
Geronimo multiwavelet with an appropriate preprocessing method and
bivariate thresholding, better results are obtained compared with
using Daubechies wavelets.

A copy can be downloaded from
http://www.stats.bris.ac.uk/~trd/threshmwave2.ps
or by emailing me at the address below

Thanks
Tim

Tim Downie Department of Mathematics
Email: Tim.Downie@bristol.ac.uk University of Bristol
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