Abstract #301408

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JSM 2002 Abstract #301408
Activity Number: 203
Type: Topic Contributed
Date/Time: Tuesday, August 13, 2002 : 10:30 AM to 12:20 PM
Sponsor: Section on Bayesian Stat. Sciences*
Abstract - #301408
Title: Robust Bayes-Minimax Incorporation of Prior Information in Wavelet Denoising Applications.
Author(s): Brani Vidakovic*+ and Claudia Angelini
Affiliation(s): Georgia Institute of Technology and CNR-IMATI
Address: 765 Ferst Drive, Atlanta, Georgia, 30332, USA
Keywords: Bayes-Minimax ; Wavelets ; Robustness
Abstract:

We propose a method for wavelet-filtering of noisy signals when prior information about the energy of the signal is available. By assuming a location-type statistical model, according to which the wavelet coefficients are treated individually, we propose a level-dependent robust shrinkage rule that turns out to be the Gamma-minimax for a suitable class Gamma of realistic priors on the wavelet coefficients corresponding to the signal part.

The proposed methodology, particularly applicable to noisy signals with a low signal-to-noise ratio, is illustrated on a battery of standard test functions. A real-life example in atomic force microscopy (AFM) is also discussed.

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Revised March 2002