Γ -Minimax Wavelet Shrinkage: A Robust Incorporation of Information about Energy of a Signal in Denoising Applications

Abstract

In this paper we propose a method for wavelet- filtering of noisy signals when prior information about the energy of the signal of interest is available. Assuming the independence model, according to which the wavelet coefficients are treated individually, we propose a level dependent shrinkage rule that turns out to be the Γ-minimax rule for a suitable class Γ of realistic priors on the wavelet coefficients. The proposed methodology, particularly applicable to noisy signals with a low signal to noise ratio, is illustrated on a battery of standard test functions. A real-life example in atomic force microscopy (AFM) is also discussed.