A Markov model for blind image separation by a mean-field EM algorithm

This paper deals with blind separation of images from noisy linear mixtures with unknown coefficients, formulated as a Bayesian estimation problem. This is a flexible framework, where any kind of prior knowledge about the source images and the mixing matrix can be accounted for. In particular, we describe local correlation within the individual images through the use of MRF image models. These are naturally suited to express the joint pdf of the sources in a factorized form, so that the statistical independence requirements of most ICA approaches to BSS are retained. Our model also includes edge variables to preserve intensity discontinuities. MRF models have been proved to be very efficient in many visual reconstruction problems, such as blind image restoration, and allow separation and edge detection to be performed simultaneously. We propose an Expectation-Maximization algorithm with the mean field approximation, to derive a procedure for estimating the mixing matrix, the sources and their edge maps. We tested this procedure on both synthetic and real images, in the fully blind case (i.e. no prior information on mixing is exploited) and found that a source model accounting for local auto-correlation is able to increase robustness against noise, even space-variant. Furthermore, when the model closely fits the source characteristics, independence is no more a strict requirement, and cross-correlated sources can be separated as well.