Wavelet Bayesian Block Shrinkage via Mixtures of Normal-Inverse Gamma Priors

Abstract

In this paper we propose a block shrinkage method in the wavelet domain for estimating an unknown function in the presence of Gaussian noise. This shrinkage utilizes an empirical Bayes, block-adaptive approach that accounts for the sparseness of the representation of the unknown function. The modeling is accomplished by using a mixture of two normal-inverse gamma (N I G) distributions as a joint prior on wavelet coefficients and noise variance in each block at a particular resolution level. This method results in explicit and fast rules. An automatic, level dependent choice for the prior hyperparameters is also suggested. Finally, the performance of the proposed method, BBS (Bayesian Block Shrinkage), is illustrated on the battery of standard test functions and compared to some standard wavelet-based denoising methods.