A semi-blind second-order approach for statistical source separation in astrophysical maps

This paper deals with a semi-blind source separation strategy which is applicable in the cases where the mixing operator can be described by just a few parameters. In these cases, unlike the independent component analysis approaches, our method only needs the covariance matrix of the data for learning the mixing operator, even if the original source processes to be separated are not totally uncorrelated. We are also able to estimate the probability density function of the source processes by a simple deconvolution procedure. Our algorithm has been tested with a database that simulates the one expected from the instruments that will operate onboard ESA's Planck Surveyor Satellite to measure the CMB anisotropies all over the celestial sphere. The assumption was made that the emission spectra of the galactic foregrounds can be parametrized, thus reducing the number of unknowns for system identification to the number of the foreground radiations. We performed separation in several sky patches, featuring different levels of galactic contamination to the CMB, and assuming several noise levels, including the ones derived from the Planck specifications. In all the cases, the CMB reconstruction was satisfactory on all the angular scales considered in the simulation; the average performance of the algorithm and its dispersion werechecked and quantified against a large set of noise patterns.