Image separation using iterated posterior point estimation

In this study, we introduce a new method for image separation problem using Monte Carlo (MC) integration method. The proposed method stands between Gibbs sampling and deterministic optimization based Iterated Conditional Mode (ICM) methods. In this sense, it incorporates the better of the two paradigms, in that it is 2 to 3 times faster than Gibbs sampling and shows better performance compared to ICM. The novelty of the method consists in the use of the conditional expectation of some robust error function as a cost function for pixels. The point estimate, that is the minimum of the robust error function, is found iteratively using a gradient descent algorithm. The stochastic gradient itself is computed using importance sampling since the posterior is not integrable analytically. Furthermore at each iteration, only the point estimates are saved, in contrast to sequential MC methods which save all of the particles (samples) of a single variable and evaluate them sequentially. The mixing matrix is estimated by the the Mean Square Error (MSE) algorithm, and the source images are modelled via Markov Random Fields (MRF).