Gamma-Minimax Wavelet Shrinkage for Signals with Low SNR
Volume 1, Issue 2 (2023), pp. 159–171
Pub. online: 29 June 2023
Type: Methodology Article
Open Access
Open Access
Area: Statistical Methodology
Accepted
15 June 2023
15 June 2023
Published
29 June 2023
29 June 2023
Abstract
In this paper, we propose a method for wavelet denoising of signals contaminated with Gaussian noise when prior information about the ${L^{2}}$-energy of the signal is available. Assuming the independence model, according to which the wavelet coefficients are treated individually, we propose simple, level-dependent shrinkage rules that turn out to be Γ-minimax for a suitable class of priors.
The proposed methodology is particularly well suited in denoising tasks when the signal-to-noise ratio is low, which is illustrated by simulations on a battery of some standard test functions. Comparison to some commonly used wavelet shrinkage methods is provided.
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