Wavelet thresholding for a wide class of noise distributions

Wavelet thresholding techniques are becoming popular in the signal processing community for denoising applications. Near-minimax properties were in particular established for simple threshold estimates over wide classes of regular functions. In this paper, we establish close connections between wavelet thresholding techniques and MAP estimation using exponential power prior distributions for a wide class of noise distributions, including heavy-tailed noises. We subsequently prove that a great variety of estimators are derived from a MAP criterion. A simulation example is presented to substantiate the proposed approach.