A Hierarchical Markov Random Field Model for Bayesian Blind Image Separation

Abstract

In this paper we propose an hierarchical Markov random field (HMRF) model and the Bayesian estimation frame for separating noisy linear mixtures of images constituted by homogeneous patches. A latent Potts-Markov labeling field is introduced for each source image to enforce piecewise homogeneity of pixel values. Based on classification labels, the upper observable intensity field is modeled by the combination of Markovian smoothness of intensity inside a patch and conditional independence at the edges. The correlation between multiple color channels, which share the same common classification, is exploited to stablize the separation process. All unknown quantities including the sources, labels, mixing coefficients and distribution hyperparameters are formulated in the Bayesian framework and estimated by MCMC simulation of their corresponding posterior laws. The performance of the proposed model is shown by experiment results on both synthetic and real images, along with some comparisons with the ICA approach.