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

In this paper we propose a method for waveletltering 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 coeÆcients are treated individually, we propose a level dependent shrinkage rule that turns out to be the -minimax rule for a suitable class of realistic priors on the wavelet coeÆcients. The proposed methodology, particularly applicable to noisy signals with a low signalto-noise ratio, is illustrated on a battery of standard test functions. A real-life example in atomic force microscopy (AFM) is also discussed.