Gamma-Minimax Wavelet Shrinkage with Three-Point Priors

04/15/2022

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by   Dixon Vimalajeewa, et al.

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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 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 the battery of standard test functions. Comparison to some standardly used wavelet shrinkage methods is provided.