Hidden Markov models for wavelet image separation and denoising

In this paper, we consider the problem of blind source separation of 2D images under a Bayesian formulation (Bayes-BSS). We transport the problem to the wavelet domain to be able to define appropriate prior distributions for the wavelet coefficients of the unobservable sources: an independent Gaussians mixture (IGM) model, a hidden Markov tree (HMT) model and contextual hidden Markov field (CHMF) model. Indeed, we consider a limiting case of the aforementioned prior models to propose a simple procedure for joint source separation and denoising. This procedure shows to be efficient, especially for highly noisy observations. Simulation examples and comparisons with standard classical methods are presented to show the performances of the proposed approach.