All-sky astrophysical component separation with Fast Independent Component Analysis (FASTICA)

We present a new, fast, algorithm for the separation of astrophysical components superposed in maps of the sky. The algorithm, based on the Independent Component Analysis (ICA) technique, is aimed at recovering both the spatial pattern and the frequency scalings of the emissions from statistically independent astrophysical processes, present along the line-of-sight, from multi-frequency observations, without any a priori assumption on properties of the components to be separated, except that all of them, except possibly one, must have non-Gaussian distributions. The analysis starts from very simple toy-models of the sky emission in order to assess the quality of the reconstruction when inputs are well known and controlled. In particular, we study the dependence of the results of separation conducted on and off the Galactic plane independently, showing that optimal separation is achieved for sky regions where components are smoothly distributed. Then we consider simulated observations of the microwave sky with angular resolution and instrumental noise, supposed to be white and stationary, at the mean nominal levels for the Planck satellite. The angular response function is assumed to be identical at each frequency since this is, up to now, one of the Fast Independent Component Analysis (FastICA) limitations. We consider several Planck observation channels containing the most important known diffuse signals: the cosmic microwave background (CMB), Galactic synchrotron, dust and free–free emissions. A method for calibrating the reconstructed maps of each component at each frequency has been devised. The spatial patterns of all the components have been recovered on all scales probed by the instrument. In particular, the CMB angular power spectra is recovered at the per cent level up to ℓmax≃2000. Frequency scalings and normalization have been recovered with better than 1 per cent precision for all the components at frequencies and in sky regions where their signal-to-noise ratio ≳1.5; the error increases at ∼10 per cent level for signal-to-noise ratios ≃1. Runs have been performed on a Pentium III 600-MHz computer; although the computing time slightly depends on the number of channels and components to be recovered, FastICA typically took about 10 min for all-sky simulations with 3.5-arcmin pixel size. Although the quoted results have been obtained under a number of simplifying assumptions, we conclude that FastICA is an extremely promising technique for analysing the maps that will be obtained by the forthcoming high-resolution CMB experiments