We present a new, fast, algorithm for the separation of astrophysical components superposed in maps of the sky, based on the fast Independent Component Analysis technique (FastICA). It allows to recover 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. We apply FastICA to simulated observations of the microwave sky with angular resolution and instrumental noise at the mean nominal levels for the Planck satellite, 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 pattern 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 percent level up to $ell_{max}simeq 2000$. Frequency scalings and normalization have been recovered with better than percent precision for all the components at frequencies and in sky regions where their signal-to-noise ratio exceeds 1.5; the error increases at ten percent level for signal-to-noise ratios about 1. Runs have been performed on a Pentium III 600 MHz computer; FastICA typically took a time of the order of 10 minutes for all-sky simulations with 3.5 arcminutes pixel size. We conclude that FastICA is an extremly promising technique for analyzing the maps that will be obtained by the forthcoming high resolution CMB experiments.
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