Gamma-Minimax Wavelet Shrinkage for Signals with Low SNR

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.