Parsimony and wavelet methods for denoising
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.