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

In this paper we propose a method for wavelet filtering of noisy signals when prior information about the L2 energy of the signal of interest is available Assuming the independence model according to which the wavelet coecients are treated individually we propose a level dependent shrinkage rule that turns out to be the ?minimax rule for a suitable class say of realistic priors on the wavelet coecients The proposed methodology is particularly well suited for denoising tasks where signal?to?noise ratio is low and it is illustrated on a battery of standard test function tions Performance comparisons with some others methods existing in the literature are provided An example in atomic force microscopy AFM is also discussed Key words and phrases? Atomic force microscopy bounded normal mean ?mini? maxity shrinkage wavelet regression