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arXiv · 2204.07544

Gamma-Minimax Wavelet Shrinkage with Three-Point Priors

Dixon Vimalajeewa·Brani Vidakovic
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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.

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Dixon Vimalajeewa, Brani Vidakovic. 2022-04-15. Gamma-Minimax Wavelet Shrinkage with Three-Point Priors. https://arxiv.org/abs/2204.07544

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