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   -> Volume 6, Issue 2


Preprint: Bayesian Wavelet Shrinkage
 
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"M.Vannucci" (m.vannucci@ukc.ac.uk)
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PostPosted: Tue Feb 11, 1997 6:15 pm    
Subject: Preprint: Bayesian Wavelet Shrinkage
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#9 Preprint: Bayesian Wavelet Shrinkage

Title: Some Findings on the Covariance Structure of Wavelet
Coefficients: Theory and Models in a Bayesian Perspective

Authors: Marina Vannucci and Fabio Corradi

Abstract: This paper refers to a wavelet shrinkage
technique. Specifically, the wavelet transform, linear and orthogonal,
permits a decomposition of noisy data into a set of wavelet
coefficients; noise is then removed by shrinking the coefficients. For
this purpose, a Bayesian approach is possible based on imposing a
statistical model on the wavelet coefficients of the unknown signal
and replacing the coefficients with the results of a Bayesian
analysis. In contrast with other Bayesian models recently proposed,
the model adopted in this paper does not assume that the wavelet
coefficients of the unknown signal are independent. Theoretical
results regarding the covariance structure of random wavelet
coefficients are presented and used to specify the Bayesian model.
Moreover, a hierarchical structure is implemented to learn about some
of the parameters of the prior distributions. Applications to
simulated signals are presented. The technique is generally applicable
to the problem of modeling wavelet coefficients and has also been used
for density estimation involving wavelets.

KEY WORDS: Non Parametric Regression, Wavelet Shrinkage, Random
Wavelet Coefficients, Bayesian Inference

If interested, download a copy from
http://stork.ukc.ac.uk/IMS/statistics/people/M.Vannucci/bayshr.ps.Z
or e-mail me at the address below. Comments are welcome.

Thanks
Marina

Marina Vannucci
Institute of Maths & Stats
University of Kent at Canterbury Phone: +44 1227 823135
Canterbury, Kent Fax: +44 1227 827932
CT2 7NF, United Kingdom E-mail: M.Vannucci@ukc.ac.uk

http://stork.ukc.ac.uk/IMS/statistics/people/M.Vannucci.html
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