ADAPTIVE BAYESIAN WAVELET SHRINKAGE

When fitting wavelet based models, shrinkage of the empirical wavelet coefficients is an effective tool for denoising the data. This article outlines a Bayesian approach to shrinkage, obtained by placing priors on the wavelet coefficients. The prior for each coefficient consists of a mixture of two normal distributions with different standard devia tions. The simple and intuitive form of prior allows us to propose aut omatic choices of prior parameters. These parameters are chosen adapti vely according to the resolution level of the coefficients, typically shrinking high resolution (frequency) coefficients more heavily. Assum ing a good estimate of the background noise level, we obtain closed fo rm expressions for the posterior means and variances of the unknown wa velet coefficients. The latter may be used to assess uncertainty in th e reconstruction. Several examples are used to illustrate the method, and comparisons are made with other shrinkage methods.