Empirical Bayesian Spatial Prediction Using Wavelets

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.KeywordsWavelet CoefficientWavelet ShrinkagePrior CovariancePseudo Maximum LikelihoodPseudo Maximum Likelihood EstimatorThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.