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

Abstract

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

Digital deblurring of CMB maps: Performance and efficient implementation

“…6). A dominating CMB component is a good approximation to real sky maps at least at medium and high Galactic latitudes where the effects of diffuse foregrounds from our Galaxy can be neglected (see Maino et al 2002, and references therein). The PSFs used in the experiments are Gaussians with FWHM similar to that expected for the PLANCK-LFI instrument.…”

“…For example, available prior information about the signals can be used in a regularised inversion via Wiener filtering and maximum entropy methods, either on small sky patches (Hobson et al 1998) or on the whole sky (Bouchet & Gispert 1999;Stolyarov et al 2002). It has been shown that under certain independence assumption on the signals, the map-operating algorithms based on Independent Component Analysis (ICA) techniques can be applied on sky patches (Baccigalupi et al 2000) as well as on the whole sky (Maino et al 2002).…”

“…Second, a better understanding of sky emissions, from foregrounds in particular, is achieved if multifrequency sky maps are compared on a common resolution. Third, some map-based component separation algorithms, such as ICA (Baccigalupi et al 2000;Maino et al 2002) require input maps with similar level of degradation. Furthermore, although the aim of satellite missions such as Planck and MAP is to obtain full sky maps of the CMB, the strength of the CMB over other backgrounds or contaminating sources will vary over the sky.…”

Of “Cocktail Parties” and Exoplanets

“…These properties have led to a surge in ICA-based analysis methods in current cosmology and extra-galactic astronomy. Here ICA is used to separate the cosmic microwave background (CMB) or signatures of distant galaxies from their galactic foregrounds (e.g., Stivoli et al 2006;Maino et al 2002Maino et al , 2007Wang et al 2010). Aumont & Macías-Pérez (2007) furthermore separate instrumental noise from the desired astrophysical signal.…”

The 2.3 GHz continuum survey of the GEM project

“…Several techniques have become available; from simple Galaxy masking of heavily contaminated regions and point sources (e.g. Mejía et al 2005) to the novel approaches of component separation and foreground removal (Hobson et al 1998;Maino et al 2002;Delabrouille et al 2003Delabrouille et al , 2009Eriksen et al 2004Eriksen et al , 2006Eriksen et al , 2008Bonaldi et al 2006;Cardoso et al 2008;Leach et al 2008;Stompor et al 2009;Ricciardi et al 2010;Fernández-Cobos et al 2012;Planck Collaboration 2013c), which exploit the spectral and spatial diversity of the different astrophysical and cosmological components. The multi-frequency design of the WMAP mission had already revealed an impressive picture of unprecedented precision of the CMB at 23 GHz, 33 GHz, 41 GHz, 61 GHz and 94 GHz (Hinshaw et al , 2012Bennett et al 2012); whereas the Planck mission, with its higher angular resolution and superb sensitivity at 30 GHz,44 GHz,70 GHz,100 GHz,143 GHz,217 GHz,353 GHz,545 GHz,and 857 GHz has, at the time of writing, made available an overwhelming set of results that push the standards of cosmological and astrophysical research to a state-of-the-art level (Planck Collaboration 2013b).…”