Bayesian wavelet denoising using Besov priors

Over the past few years, there has been a great research interest in thresholding methods for nonlinear wavelet regression over spaces of smooth functions. Near-minimax convergence rates were in particular established for simple hard and soft thresholding rules over Besov and Triebel bodies. In this paper, we propose a Bayesian approach where the functional properties of the underlying signal in noise are directly modeled using Besov norm priors on its wavelet decomposition coefficients. A Gibbs sampler is subsequently presented to estimate the model parameters and the posterior mean of the signal in the case of possibly non-Gaussian noise.