Separation of Correlated Astrophysical Sources Using Multiple-Lag Data Covariance Matrices
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Separation of Correlated Astrophysical Sources Using Multiple-Lag Data Covariance Matrices L. Bedini Istituto di Scienza e Tecnologie dell’Informazione, CNR, Area della Ricerca di Pisa, via G. Moruzzi 1, 56124 Pisa, Italy Email: [email protected]
D. Herranz Istituto di Scienza e Tecnologie dell’Informazione, CNR, Area della Ricerca di Pisa, via G. Moruzzi 1, 56124 Pisa, Italy Email: [email protected]
E. Salerno Istituto di Scienza e Tecnologie dell’Informazione, CNR, Area della Ricerca di Pisa, via G. Moruzzi 1, 56124 Pisa, Italy Email: [email protected]
C. Baccigalupi International School for Advanced Studies, via Beirut 4, 34014 Trieste, Italy Email: [email protected]
˘ E. E. Kuruoglu Istituto di Scienza e Tecnologie dell’Informazione, CNR, Area della Ricerca di Pisa, via G. Moruzzi 1, 56124 Pisa, Italy Email: [email protected]
A. Tonazzini Istituto di Scienza e Tecnologie dell’Informazione, CNR, Area della Ricerca di Pisa, via G. Moruzzi 1, 56124 Pisa, Italy Email: [email protected] Received 8 June 2004; Revised 18 October 2004 This paper proposes a new strategy to separate astrophysical sources that are mutually correlated. This strategy is based on secondorder statistics and exploits prior information about the possible structure of the mixing matrix. Unlike ICA blind separation approaches, where the sources are assumed mutually independent and no prior knowledge is assumed about the mixing matrix, our strategy allows the independence assumption to be relaxed and performs the separation of even significantly correlated sources. Besides the mixing matrix, our strategy is also capable to evaluate the source covariance functions at several lags. Moreover, once the mixing parameters have been identified, a simple deconvolution can be used to estimate the probability density functions of the source processes. To benchmark our algorithm, we used a database that simulates the one expected from the instruments that will operate onboard ESA’s Planck Surveyor Satellite to measure the CMB anisotropies all over the celestial sphere. Keywords and phrases: statistical, image processing, cosmic microwave background.
1.
INTRODUCTION
Separating the individual radiations from the measured signals is a common problem in astrophysical data analysis [1]. As an example, in cosmic microwave background anisotropy surveys, the cosmological signal is normally combined with foreground radiations from both extragalactic and galactic sources, such as the Sunyaev-Zeldovich effects from clusters of galaxies, the effect of the individual galaxies, the emis-
sion from galactic dust, the galactic synchrotron and freefree emissions. If one is only interested in estimating the CMB anisotropies, the interfering signals can just be treated as noise, and reduced by suitable cancellation procedures. However, the foregrounds have an interest of their own, and it could be useful to extract all of them from multichannel data, by exploiting their different emission spectra. Some authors [2, 3] have tried to
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