Approaches to wavelet-based denoising (or signal enhancement) have generally 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 (MMDL) principle. We first determine the least favorable distribution in the /spl epsiv/-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, together constitute a saddle point. The MMDL approach results in a thresholding scheme that is resistant to heavy tailed noise. We further extend this framework and propose a novel approach to selecting an adapted or best basis (BB) that results in optimal signal reconstruction. Finally, 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.

Some wavelet-based methods for signal estimation in the presence of noise are reviewed in the context of the parsimonious representation of the underlying signal. Three approaches are considered. The first is based on the application of the minimum description length (MDL) principle. The robustness of this method is improved in the second approach, by relaxing the assumption of known noise distribution following Huber's (1967) work. In the third approach, a Bayesian strategy is adopted in order to incorporate prior information pertaining to the signal of interest; this method is especially useful at low signal-to-noise ratios.

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 /spl epsi/-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.