Abstract
Wavelet shrinkage methods, introduced by Donoho and John-stone (1994, 1995, 1998) and Donoho et al. (1995), are a powerful way to carry out signal denoising, especially when the underlying signal has a sparse wavelet representation. Wavelet shrinkage based on the Bayesian approach involves specifying a prior distribution for the wavelet coefficients. In this chapter, we consider a Gaussian prior with nonzero means for wavelet coefficients, which is different from other priors used in the literature. An empirical Bayes approach is taken by estimating the mean parameters using Q-Q plots, and the hyperparameters of the prior covariance are estimated by a pseudo maximum likelihood method. A simulation study shows that our empirical Bayesian spatial prediction approach outperforms the well known VisuShrink and SureShrink methods for recovering a wide variety of signals.