In this paper we review a maximum a posteriori (MAP) approach detection method in a Bayesian scheme which incorporates prior information about the source flux distribution, the locations and the number of sources of extragalactic point sources in images of the Cosmic Microwave Background. This new technique allows us to obtain fast solutions and to fix the number of detected sources in a non-arbitrary way. The performance of the method is superior to that of the standard frequentist approach based on the matched filter.

We propose to model the image differentials of astrophysical source maps by Student's t-distribution and to use them in the Bayesian source separation method as priors. We introduce an efficient Markov Chain Monte Carlo (MCMC) sampling scheme to unmix the astrophysical sources and describe the derivation details. In this scheme, we use the Langevin stochastic equation for transitions, which enables parallel drawing of random samples from the posterior, and reduces the computation time significantly (by two orders of magnitude). In addition, Student's t-distribution parameters are updated throughout the iterations. The results on astrophysical source separation are assessed with two performance criteria defined in the pixel and the frequency domains.

Within the framework of wavelet analysis, we describe a novel technique for removing noise from astrophysical images. We design a Bayesian estimator, which relies on a particular member of the family of isotropic /spl alpha/-stable distributions, namely the bivariate Cauchy density. Using the bivariate Cauchy model we develop a noise-removal processor that takes into account the interscale dependencies of wavelet coefficients. We show through simulations that our proposed technique outperforms existing methods both visually and in terms of root mean squared error.