Separation of correlated astrophysical sources using multiple-lag data covariance matrices

This paper deals with a source separation strategy based on second-order statistics, namely, on data covariance matrices estimated at several lags. In general, ``blind'' approaches to source separation do not assume any knowledge on the mixing operator; however, any prior information about the possible structure of the mixing operator can improve the solution. Unlike ICA blind separation approaches, where mutual independence between the sources is assumed, our method only needs to constrain second-order statistics, and is effective even if the original sources are significantly correlated. Besides the mixing matrix, our strategy is also capable to evaluate the source covariance functions at several lags. Moreover, once the mixing parameters have been identified, a simple deconvolution can be used to estimate the probability density functions of the source processes. To benchmark our algorithm, we used 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 parametrised, 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.