2002
Journal article
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All-sky astrophysical component separation with fast independent
Maino D, Farusi A, Baccigalupi C, Perrotta F, Banday Aj, Bedini L, Burigana C, De Zotti G, Gorski Km, Salerno EWe 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 freefree 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 l_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.Source: MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY (PRINT), vol. 334, pp. 53-68
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2004
Journal article
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Extracting cosmic microwave background polarization from satellite astrophysical maps
Baccigalupi C, Perrotta F, De Zotti G, Smoot Gf, Burigana C, Maino D, Bedini L, Salerno EWe present the application of the fast independent component analysis (FASTICA) technique for blind component separation to polarized astrophysical emission. We study how the cosmic microwave background (CMB) polarized signal, consisting of E and B modes, can be extracted from maps affected by substantial contamination from diffuse galactic foreground emission and instrumental noise. We implement Monte Carlo chains varying the CMB and noise realizations in order to assess the average capabilities of the algorithm and their variance. We perform the analysis of all-sky maps simulated according to the Planck satellite capabilities, modelling the sky signal as a superposition of teh CMB and of the existing simulated polarization templates of galactic synchrotron. Our results indicate that teh angular power spectrum of CMB E mode can be recovered an all scales up to l=1000, corresponding to the fourth acoustic oscillation, while the B-mode power spectrum can be detected, up to its turnover al l=100, if the ratio of tensor to scalar contributions to the temperature quadrupole exceeds 30 percent. The power spectrum of the cross-correlation between total intensity and polarization, TE, can be recovered up to l=1200, corresponding to the seventh TE acoustic oscillation.Source: MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY (PRINT), vol. 354 (issue 1), pp. 55-70
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2006
Journal article
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Estimating the spectral indices of correlated astrophysical foregrounds by a second-order statistical approach
Bonaldi A, Bedini L, Salerno E, Baccigalupi C, De Zotti GWe 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.Source: MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY (PRINT), vol. 373 (issue 1), pp. 271-279
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2007
Conference article
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Blind source separation applied to spectral unmixing: comparing different measures of nongaussianity
Caiafa C F, Salerno E, Proto A NWe report some of our results of a particular blind source separation technique applied to spectral unmixing of remote-sensed hyperspectral images. Different nongaussianity measures are introduced in the learning procedure, and the results are compared to assess their relative efficiencies, with respect to both the output signal-to-interference ratio and the overall computational complexity. This study has been conducted on both simulated and real data sets, and the first results show that skewness is a powerful and unexpensive tool to extract the typical sources that charcterize remote-sensed images.
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2007
Conference article
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Extracting astrophysical sources from channel-dependent convolutional mixtures by correlated component analysis in the frequency domain
Bedini L, Salerno EA second-order statistical technique (FD-CCA) for semi-blind source separation from multiple-sensor data is presented. It works in the Fourier domain and allows us to both learn the unknown mixing operator and estimate the source cross-spectra before applying the proper source separation step. If applied to small sky patches, our algorithm can be used to extract diffuse astrophysical sources from the mixed maps obtained by radioastronomical surveys, even though their resolution depends on the measurement channel. Unlike the independent component analysis approach, FD-CCA does not need mutual independence between sources, but exploits their spatial autocorrelations. We describe our algorithm, derived from a previous pixel-domain strategy, and present some results from simulated data.
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2008
Journal article
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Component separation methods for the PLANCK mission
Leach S M, Cardoso J, Baccigalupi C, Barreiro R B, Betoule M, Bobin J, Bonaldi A, Delabrouille J, De Zotti G, Dickinson C, Eriksen H K, Gonzaleznuevo J, Hansen F K, Herranz D, Le Jeune M, Lopezcaniego M, Martinezgonzalez E, Massardi M, Melin J, Mivilledechêne M, Patanchon G, Prunet S, Ricciardi S, Salerno E, Sanz J L, Stark J, Stivoli F, Stolyarov V, Stompor R, Vielva PContext. 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. Aims. The goal of this paper is to compare proposed methods for separating CMB from foregrounds based on their di?erent spectral and spatial characteristics, and to separate the foregrounds into "components" with di?erent physical origins (Galactic synchrotron, free-free and dust emissions; extra-galactic and far-IR point sources; Sunyaev-Zeldovich e?ect, etc.). Methods. A component separation challenge has been organised, 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. Results. Di?erent methods proved to be e?ective in cleaning the CMB maps of foreground contamination, in reconstructing maps of di?use 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 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 e?ect on two thirds of the sky.We have found that no single method performs best for all scientific objectives. Conclusions. We foresee that the final component separation pipeline for planck will involve a combination of methods and iterations between processing steps targeted at di?erent objectives such as di?use component separation, spectral estimation, and compact source extraction.Source: ASTRONOMY & ASTROPHYSICS (PRINT), vol. 491 (issue 2), pp. 597-615
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2010
Journal article
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Correlated component analysis for diffuse component separation with error estimation on simulated Planck polarization data
Ricciardi S, Bonaldi A, Natoli P, Polenta G, Baccigalupi C, Salerno E, Kayabol K, Bedini L, De Zotti GWe present a data analysis pipeline for cosmic microwave background (CMB) polarization experiments, running from multifrequency maps to the power spectra. We focus mainly on component separation and, for the first time, we work out the covariance matrix accounting for errors associated with the separation itself. This allows us to propagate such errors and evaluate their contributions to the uncertainties on the final products. The pipeline is optimized for intermediate and small scales, but could be easily extended to lower multipoles.We exploit realistic simulations of the sky, tailored for the Planck mission. The component separation is achieved by exploiting the correlated component analysis in the harmonic domain, which we demonstrate to be superior to the real-space application.We present two techniques to estimate the uncertainties on the spectral parameters of the separated components. The component separation errors are then propagated by means of Monte Carlo simulations to obtain the corresponding contributions to uncertainties on the component maps and on the CMB power spectra. For the Planck polarization case they are found to be subdominant compared to noise.Source: MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY (PRINT), vol. 406 (issue 3), pp. 1644-1658
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2006
Journal article
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Particle swarm optimization for the reconstruction of permittivity range profiles from microwave measurements
Genovesi S, Salerno EAt the Signal and Images lab, ISTI-CNR, we are developing a new algorithm to reconstruct the permittivity range profile of a layered medium from microwave backscattering data. The algorithm is based on a particle swarm strategy to optimize a specific edge-preserving objective functional. Our technique is able to efficiently find the global optimum of the objective functional, while preserving the discontinuities in the reconstructed profile.Source: ERCIM NEWS, vol. 64, pp. 42-43
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2010
Contribution to journal
Open Access
High-resolution microwave diagnostics of architectural components by particle swarm optimization
Genovesi S, Salerno E, Monorchio A, Manara GWe present a very simple monostatic setup for coherent multifrequency microwave measurements, and an optimization procedure to reconstruct high-resolution permittivity profiles of layered objects from complex reflection coefficients. This system is capable of precisely locating internal inhomogeneities in dielectric bodies, and can be applied to on-site diagnosis of architectural components. While limiting the imaging possibilities to 1D permittivity profiles, the monostatic geometry has an important advantage over multistatic tomographic systems, since these are normally confined to laboratories, and on-site applications are difficult to devise. The sensor is a transmitting-receiving microwave antenna, and the complex reflection coefficients are measured at a number of discrete frequencies over the system passband by using a general-purpose vector network analyzer. A dedicated instrument could also be designed, thus realizing an unexpensive, easy-to-handle system. The profile reconstruction algorithm is based on the optimization of an objective functional that includes a data-fit term and a regularization term. The first consists in the norm of the complex vector difference between the measured data and the data computed by a forward solver from the current estimate of the profile function. The regularization term enforces a piecewise smooth model for the solution, based on two 1D interacting Markov random fields: the intensity field, which models the continuous permittivity values, and the binary line field, which accounts for the possible presence of discontinuities in the profile. The data-fit and the regularization terms are balanced through a tunable regularization coefficient. By virtue of this prior model, the final result is robust against noise, and overcomes the usual limitations in spatial resolution induced by the wavelengths of the probing radiations. Indeed, the accuracy in the location of the discontinuities is only limited by the system noise and the discretization grid used by the forward solver. The algorithm we chose to optimize the objective is based on the particle swarm paradigm. Each feasible solution is coded as a location in a multidimensional space, explored by a number of "particles" each moving with a certain velocity, which is partly random and partly induced by the experience of both the particle itself and the "swarm" of all the other particles. In our case, the search is complicated by the mixed continuous-binary nature of our unknowns, but the swarm intelligence approach maintains the advantage of its intrinsic parallelism. The experimental results we obtained from both simulated and real measurements show that, for typical permittivity values and radiation wavelengths, the spatial resolution is highly improved by the line process. From real measurements in the range 1.7-2.6 GHz, we accurately reconstructed the permittivity values of our test phantom and located the discontinuities within the limits imposed by our discretization grid (with 1.5 mm cell thickness). At present, the applicability of our reconstruction method is still limited by the forward solver, which is based on a cascaded transmission-line model that assumes normal and plane-wave incidence. We are developing a new solver based on a closed-form Green's function in multilayered media, which should enable us to model appropriately both the microwave sensor and the illumination geometry, thus improving the accuracy of the computed reflection coefficients in the objective functional.Source: GEOPHYSICAL RESEARCH ABSTRACTS (ONLINE), vol. 12
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2010
Contribution to book
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'Blind' does not mean visually challenged: extracting source signals from mixed data
Salerno EThis paper introduces the problem of blind source separation, a phrase that denotes a class of techniques aimed at estimating signals when the physical system through which they are sensed is not known. The solution to this problem thus entails both system identification and signal estimation. Actually, I show that any lack of information on the physical system must be replaced by information on signals, and that, although a reliable data model is lacking, many pieces of information are used to constrain it. I only introduce some basic principles, with just a few details on the techniques used in practice, but the bibliography can help the reader to deepen their understanding of the matter. Most of the material is introduced by examples.
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