Wavelet Bayesian block shrinkage via mixtures of normal-inverse gamma priors

This article proposes a nonlinear block shrinkage method in the wavelet domain for estimating an unknown function in the presence of Gaussian noise. This shrinkage uses an empirical Bayesian blocking 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 (NIG) distributions as a joint prior on wavelet coefficients and noise variance in each block at a particular resolution level. This method results in an explicit and readily implementable weighted sum of shrinkage rules. An automatic, level-dependent choice for the model hyperparameters, that leads to amplitude-scale invariant solutions, 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 existing block-wavelet denoising methods.