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Register a new userComponent separation with flexible models. Application to the separation of astrophysical emissions
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Added by
Jean-Francois Cardoso
Publication date
2008
fields
Physics
and research's language is
English
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This paper offers a new point of view on component separation, based on a model of additive components which enjoys a much greater flexibility than more traditional linear component models. This flexibility is needed to process the complex full-sky observations of the CMB expected from the Planck space mission, for which it was developed, but it may also be useful in any context where accurate component separation is needed.
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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.
The Internal Linear Combination (ILC) component separation method has been extensively used to extract a single component, the CMB, from the WMAP multifrequency data. We generalise the ILC approach for separating other millimetre astrophysical emissions. We construct in particular a multidimensional ILC filter, which can be used, for instance, to estimate the diffuse emission of a complex component originating from multiple correlated emissions, such as the total emission of the Galactic interstellar medium. The performance of such generalised ILC methods, implemented on a needlet frame, is tested on simulations of Planck mission observations, for which we successfully reconstruct a low noise estimate of emission from astrophysical foregrounds with vanishing CMB and SZ contamination.
A flexible maximum-entropy component separation algorithm is presented that accommodates anisotropic noise, incomplete sky-coverage and uncertainties in the spectral parameters of foregrounds. The capabilities of the method are determined by first applying it to simulated spherical microwave data sets emulating the COBE-DMR, COBE-DIRBE and Haslam surveys. Using these simulations we find that is very difficult to determine unambiguously the spectral parameters of the galactic components for this data set due to their high level of noise. Nevertheless, we show that is possible to find a robust CMB reconstruction, especially at the high galactic latitude. The method is then applied to these real data sets to obtain reconstructions of the CMB component and galactic foreground emission over the whole sky. The best reconstructions are found for values of the spectral parameters: T_d=19 K, alpha_d=2, beta_ff=-0.19 and beta_syn=-0.8. The CMB map has been recovered with an estimated statistical error of sim 22 muK on an angular scale of 7 degrees outside the galactic cut whereas the low galactic latitude region presents contamination from the foreground emissions.
The polarization modes of the cosmological microwave background are an invaluable source of information for cosmology, and a unique window to probe the energy scale of inflation. Extracting such information from microwave surveys requires disentangling between foreground emissions and the cosmological signal, which boils down to solving a component separation problem. Component separation techniques have been widely studied for the recovery of CMB temperature anisotropies but quite rarely for the polarization modes. In this case, most component separation techniques make use of second-order statistics to discriminate between the various components. More recent methods, which rather emphasize on the sparsity of the components in the wavelet domain, have been shown to provide low-foreground, full-sky estimate of the CMB temperature anisotropies. Building on sparsity, the present paper introduces a new component separation technique dubbed PolGMCA (Polarized Generalized Morphological Component Analysis), which refines previous work to specifically tackle the estimation of the polarized CMB maps: i) it benefits from a recently introduced sparsity-based mechanism to cope with partially correlated components, ii) it builds upon estimator aggregation techniques to further yield a better noise contamination/non-Gaussian foreground residual trade-off. The PolGMCA algorithm is evaluated on simulations of full-sky polarized microwave sky simulations using the Planck Sky Model (PSM), which show that the proposed method achieve a precise recovery of the CMB map in polarization with low noise/foreground contamination residuals. It provides improvements with respect to standard methods, especially on the galactic center where estimating the CMB is challenging.
The Planck satellite will map the full sky at nine frequencies from 30 to 857 GHz. The CMB intensity and polarization that are its prime targets are contaminated by foreground emission. The goal of this paper is to compare proposed methods for separating CMB from foregrounds based on their different spectral and spatial characteristics, and to separate the foregrounds into components of different physical origin. A component separation challenge has been organized, based on a set of realistically complex simulations of sky emission. Several methods including those based on internal template subtraction, maximum entropy method, parametric method, spatial and harmonic cross correlation methods, and independent component analysis have been tested. Different methods proved to be effective in cleaning the CMB maps from foreground contamination, in reconstructing maps of diffuse Galactic emissions, and in detecting point sources and thermal Sunyaev-Zeldovich signals. The power spectrum of the residuals is, on the largest scales, four orders of magnitude lower than that of the input Galaxy power spectrum at the foreground minimum. The CMB power spectrum was accurately recovered up to the sixth acoustic peak. The point source detection limit reaches 100 mJy, and about 2300 clusters are detected via the thermal SZ effect on two thirds of the sky. We have found that no single method performs best for all scientific objectives. We foresee that the final component separation pipeline for Planck will involve a combination of methods and iterations between processing steps targeted at different objectives such as diffuse component separation, spectral estimation and compact source extraction.
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