Gamma-Minimax Wavelet Shrinkage with Three-Point Priors

TL;DR

This paper introduces a gamma-minimax wavelet shrinkage method using three-point priors for denoising signals with Gaussian noise, especially effective at low signal-to-noise ratios, demonstrated through simulations.

Contribution

It presents a novel level-dependent shrinkage rule that is gamma-minimax for a class of priors, improving wavelet denoising performance under specific prior information.

Findings

Effective in low SNR conditions

Outperforms standard wavelet shrinkage methods

Demonstrated through simulations on test functions

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 a simple, level dependent shrinkage rules that turn out to be $\Gamma$-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 the battery of standard test functions. Comparison to some standardly used wavelet shrinkage methods is provided.