Gamma-Minimax Wavelet Shrinkage for Signals with Low SNR

Vimalajeewa, Dixon; DasGupta, Anirban; Ruggeri, Fabrizio; Vidakovic, Brani

doi:10.51387/23-NEJSDS43

The New England Journal of Statistics in Data Science

Gamma-Minimax Wavelet Shrinkage for Signals with Low SNR

Volume 1, Issue 2 (2023), pp. 159–171

Dixon Vimalajeewa Anirban DasGupta Fabrizio Ruggeri All authors (4)

https://doi.org/10.51387/23-NEJSDS43

Pub. online: 29 June 2023 Type: Statistical Methodology

Open Access

Accepted
15 June 2023

Published
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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Keywords

Wavelet Regression Shrinkage Bounded Normal Mean Γ-minimaxity Least Favorable Prior Contamination Class Low Signal-to-Noise Ratio

Funding

The work of Dixon Vimalajeewa was supported by H. O. Hartley endowment at Texas A&M University.

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