Independent factor analysis for component separation from planck channel maps

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. This task is made difficult by our insufficient knowledge of the weights to be given to the individual signals at different frequencies. 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, had 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 the expectation-maximization and the simulated annealing learning algorithm in the estimation of the mixing parameters. The simulation results demonstrate the success of the independent factor analysis approach with simulated-annealing learning, which proves better than the expectation-maximization learning especially for higher noise levels and when the independence of the performance from starting points is considered.