We propose a Bayesian approach to joint source separation and restoration for astrophysical diffuse sources. We constitute a prior statistical model for the source images by using their gradient maps. We assume a t-distribution for the gradient maps
in different directions, because it is able to fit both smooth and sparse data. A Monte Carlo technique, called Langevin sampler, is used to estimate the source images and all the model parameters are estimated by using deterministic techniques.
We propose to model the image differentials of astrophysical source maps by Students 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, Students 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.
We present a new method based on the N-point probability distribution (pdf) to study non-Gaussianity in cosmic microwave background (CMB) maps. Likelihood and Bayesian estimation are applied to a local non-linear perturbed model up to third order, ch
aracterized by a linear term which is described by a Gaussian N-pdf, and a second and third order terms which are proportional to the square and the cube of the linear one. We also explore a set of model selection techniques (the Akaike and the Bayesian Information Criteria, the minimum description length, the Bayesian Evidence and the Generalized Likelihood Ratio Test) and their application to decide whether a given data set is better described by the proposed local non-Gaussian model, rather than by the standard Gaussian temperature distribution. As an application, we consider the analysis of the WMAP 5-year data at a resolution of around 2 degrees. At this angular scale (the Sachs-Wolfe regime), the non-Gaussian description proposed in this work defaults (under certain conditions) to an approximative local form of the weak non-linear coupling inflationary model (e.g. Komatsu & Spergel 2001) previously addressed in the literature. For this particular case, we obtain an estimation for the non-linear coupling parameter of -94 < F_nl < 154 at 95% CL. Equally, model selection criteria also indicate that the Gaussian hypothesis is favored against the particular local non-Gaussian model proposed in this work. This result is in agreement with previous findings obtained for equivalent non-Gaussian models and with different non-Gaussian estimators. However, our estimator based on the N-pdf is more efficient than previous estimators and, therefore, provides tighter constraints on the coupling parameter at degree angular resolution.
In this paper we introduce a new linear filtering technique, the so-called matrix filters, that maximizes the signal-to-interference ratio of compact sources of unknown intensity embedded in a set of images by taking into account the cross-correlatio
ns between the different channels. By construction, the new filtering technique outperforms (or at least equals) the standard matched filter applied on individual images. An immediate application is the detection of extragalactic point sources in Cosmic Microwave Background images obtained at different wavelengths. We test the new technique in two simulated cases: a simple two-channel case with ideal correlated color noise and more realistic simulations of the sky as it will be observed by the LFI instrument of the upcoming ESAs Planck mission. In both cases we observe an improvement with respect to the standard matched filter in terms of signal-to-noise interference, number of detections and number of false alarms.
