To cite this version:Koray Kayabol, Josiane Zerubia. This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication.

Abstract-We investigate the source separation problem of random fields within a Bayesian framework. The Bayesian formulation enables the incorporation of prior image models in the estimation of sources. Due to the intractability of the analytical solution, we resort to numerical methods for the joint maximization of the a posteriori distribution of the unknown variables and parameters. We construct the prior densities of pixels using Markov random fields based on a statistical model of the gradient image, and we use a fully Bayesian method with modified-Gibbs sampling. We contrast our work to approximate Bayesian solutions such as Iterated Conditional Modes (ICM) and to non-Bayesian solutions of ICA variety. The performance of the method is tested on synthetic mixtures of texture images and astrophysical images under various noise scenarios. The proposed method is shown to outperform significantly both its approximate Bayesian and non-Bayesian competitors.

We present a data analysis pipeline for cosmic microwave background (CMB) polarization experiments, running from multifrequency maps to the power spectra. We focus mainly on component separation and, for the first time, we work out the covariance matrix accounting for errors associated with the separation itself. This allows us to propagate such errors and evaluate their contributions to the uncertainties on the final products. The pipeline is optimized for intermediate and small scales, but could be easily extended to lower multipoles. We exploit realistic simulations of the sky, tailored for the Planck mission. The component separation is achieved by exploiting the correlated component analysis in the harmonic domain, which we demonstrate to be superior to the real-space application. We present two techniques to estimate the uncertainties on the spectral parameters of the separated components. The component separation errors are then propagated by means of Monte Carlo simulations to obtain the corresponding contributions to uncertainties on the component maps and on the CMB power spectra. For the Planck polarization case they are found to be subdominant compared to noise

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