A B S T R A C TWe 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-ofsight, 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 ' max . 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. P

We implement an independent component analysis (ICA) algorithm to separate signals of different origin in sky maps at several frequencies. Owing to its self‐organizing capability, it works without prior assumptions on either the frequency dependence or the angular power spectrum of the various signals; rather, it learns directly from the input data how to identify the statistically independent components, on the assumption that all but, at most, one of the components have non‐Gaussian distributions. We have applied the ICA algorithm to simulated patches of the sky at the four frequencies (30, 44, 70 and 100 GHz) used by the Low Frequency Instrument of the European Space Agency's Planck satellite. Simulations include the cosmic microwave background (CMB), the synchrotron and thermal dust emissions, and extragalactic radio sources. The effects of the angular response functions of the detectors and of instrumental noise have been ignored in this first exploratory study. The ICA algorithm reconstructs the spatial distribution of each component with rms errors of about 1 per cent for the CMB, and 10 per cent for the much weaker Galactic components. Radio sources are almost completely recovered down to a flux limit corresponding to ≃0.7σCMB, where σCMB is the rms level of the CMB fluctuations. The signal recovered has equal quality on all scales larger than the pixel size. In addition, we show that for the strongest components (CMB and radio sources) the frequency scaling is recovered with per cent precision. Thus, algorithms of the type presented here appear to be very promising tools for component separation. On the other hand, we have been dealing here with a highly idealized situation. Work to include instrumental noise, the effect of different resolving powers at different frequencies and a more complete and realistic characterization of astrophysical foregrounds is in progress.

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We present the first tests of a new method, the correlated component analysis (CCA) based on second-order statistics, to estimate the mixing matrix, a key ingredient to separate astrophysical foregrounds superimposed to the Cosmic Microwave Background (CMB). In the present application, the mixing matrix is parametrized in terms of the spectral indices of Galactic synchrotron and thermal dust emissions, while the free-free spectral index is prescribed by basic physics, and is thus assumed to be known. We consider simulated observations of the microwave sky with angular resolution and white stationary noise at the nominal levels for the Planck satellite, and realistic foreground emissions, with a position-dependent synchrotron spectral index. We work with two sets of Planck frequency channels: the low-frequency set, from 30 to 143 GHz, complemented with the Haslam 408 MHz map, and the high-frequency set, from 217 to 545 GHz. The concentration of intense free-free emission on the Galactic plane introduces a steep dependence of the spectral index of the global Galactic emission with Galactic latitude, close to the Galactic equator. This feature makes difficult for the CCA to recover the synchrotron spectral index in this region, given the limited angular resolution of Planck, especially at low frequencies. A cut of a narrow strip around the Galactic equator (|b| < 3 • ), however, allows us to overcome this problem. We show that, once this strip is removed, the CCA allows an effective foreground subtraction, with residual uncertainties inducing a minor contribution to errors on the recovered CMB power spectrum.