Source separation in astrophysical maps using independent factor analysis.
A microwave sky map results from a combination of signals from various astrophysical sources, such as cosmic microwave background radiation, synchrotron radiation and galactic dust radiation. To derive information about these sources, one needs to separate them from the measured maps on different frequency channels. Our insufficient knowledge of the weights to be given to the individual signals at different frequencies makes this a difficult task. Recent work on the problem led to only limited success due to ignoring the noise and to the lack of a suitable statistical model for the sources. In this paper, we derive the statistical distribution of some source realizations, and check the appropriateness of a Gaussian mixture model for them. A source separation technique, namely, independent factor analysis, has been suggested recently in the literature for Gaussian mixture sources in the presence of noise. This technique employs a three layered neural network architecture which allows a simple, hierarchical treatment of the problem. We modify the algorithm proposed in the literature to accommodate for space-varying noise and test its performance on simulated astrophysical maps. We also compare the performances of an expectation-maximization and a simulated annealing learning algorithm in estimating the mixture matrix and the source model parameters. The problem with expectation-maximization is that it does not ensure global optimization, and thus the choice of the starting point is a critical task. Indeed, we did not succeed to reach good solutions for random initializations of the algorithm. Conversely, our experiments with simulated annealing yielded initialization-independent results. The mixing matrix and the means and coefficients in the source model were estimated with a good accuracy while some of the variances of the components in the mixture model were not estimated satisfactorily.
Kuruoğlu
Ercan E
EE
Istituto di Scienza e Tecnologie dell'Informazione Consiglio Nazionale delle Ricerche, Area della Ricerca CNR di Pisa, via G. Moruzzi 1, 56124, Pisa, Italy. kuruoglu@iei.pi.cnr.it
Bedini
Luigi
L
Paratore
Maria T
MT
Salerno
Emanuele
E
Tonazzini
Anna
A
D001256:Astronomy / Q000379:methods* / Q000706:statistics & numerical data; D005163:Factor Analysis, Statistical; D010825:Physics / Q000379:methods* / Q000706:statistics & numerical data