Abstract
This paper proposes a new strategy to separate astrophysical sources that are mutually correlated. This strategy is based on second-order 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.
Highlights
Separating the individual radiations from the measured signals is a common problem in astrophysical data analysis [1]
The source maps we considered were the CMB anisotropy, the galactic synchrotron, and thermal dust emissions over the four measurement channels centred at 30 GHz, 44 GHz, 70 GHz, and 100 GHz
By exploiting the spatial structure of the sources, we developed an identification and separation algorithm that is able to exploit any available information on possible structure of the mixing matrix and the source covariance matrices
Summary
Separating the individual radiations from the measured signals is a common problem in astrophysical data analysis [1]. The problem of estimating all the model parameters and source signals cannot be solved by just using second-order statistics, since these are only able to enforce uncorrelation This has been done in special cases, where additional hypotheses on the spatial correlations or, equivalently, on the spectra of the individual signals are assumed [9, 14, 15]. If we know the noise covariance matrix, we are able to write a number of relationships from which the unknown parameters can be estimated This is what is done by the second-order blind identification (SOBI) algorithm presented in [15]. In our particular case being able to parametrise the mixing matrix allows us to substantially reduce the number of unknowns This permits to improve the performance of our technique. We give some remarks and future directions
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