Robust wavelet thresholding for noise suppression

Approaches to wavelet-based denoising (or signal enhancement) have so far relied on the assumption of normally distributed perturbations. To relax this assumption, which is often violated in practice, we derive a robust wavelet thresholding technique based on the minimax description length principle. We first determine the least favorable distribution in the ε-contaminated normal family as the member that maximizes the entropy. We show that this distribution and the best estimate based upon it, namely the maximum likelihood estimate, constitute a saddle point. This results in a threshold that is more resistant to heavy-tailed noise, but for which the estimation error is still potentially unbounded. We address the practical case where the underlying signal is known to be bounded, and derive a two-sided thresholding technique that is resistant to outliers and has bounded error. We provide illustrative examples