Wavelets and Markov Random Fields in a Bayesian Framework

The paper introduces a Bayesian framework for wavelet coefficients. Particularly aimed at efficient implementations and at higher-dimensional wavelet transforms, the method is based on a Markov Random Field description of the coefficients. The Bayesian approach allows to impose various types of constraints on the interactions of coefficients that are neighbours in the MRF. Several applications that are based on a manipulation of wavelet coefficients can benefit from this approach. This is illustrated with an example.