Γ -Minimax Wavelet Shrinkage: A Robust Incorporation of Information about Energy of a Signal in Denoising Applications

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Title: Γ -Minimax Wavelet Shrinkage: A Robust Incorporation of Information about Energy of a Signal in Denoising Applications
Alternative Title: Γ-Minimax Wavelet Shrinkage
Author: Angelini, Claudia ; Vidakovic, Brani
Abstract: In this paper we propose a method for wavelet- filtering of noisy signals when prior information about the energy of the signal of interest is available. Assuming the independence model, according to which the wavelet coefficients are treated individually, we propose a level dependent shrinkage rule that turns out to be the Γ-minimax rule for a suitable class Γ of realistic priors on the wavelet coefficients. 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.
Type: Technical Report
URI: http://hdl.handle.net/1853/25933
Date: 2001
Contributor: Georgia Institute of Technology
Consiglio nazionale delle ricerche (Italy). Istituto per Applicazioni della Matematica
Relation: Biomedical Engineering Technical Report ; G06/2001
Publisher: Georgia Institute of Technology
Subject: Wavelet regression
Shrinkage
Bounded normal mean
Γ -minimaxity
Atomic force microscopy

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