Neural networks and the separation of cosmic microwave background and astrophysical signals in sky maps

We implement an independent component analysis (ICA) algorithm to separate signals of different origin in sky maps at several frequencies. Owing to it s self-organizing capability, it works without prior assumptions on either the frequency dependence or the angular power spectrum of the various signa ls; rather, it learns directly from the input data how to identify the stat istically independent components, on the assumption that all but, at most, one of the components have non-Gaussian distributions. We have applied the ICA algorithm to simulated patches of the sky at the fo ur frequencies (30, 44, 70 and 100 GHz) used by the Low Frequency Instrumen t of the European Space Agency's Planck satellite. Simulations include the cosmic microwave background (CMB), the synchrotron and thermal dust emissio ns, and extragalactic radio sources. The effects of the angular response fu nctions of the detectors and of instrumental noise have been ignored in thi s first exploratory study. The ICA algorithm reconstructs the spatial distr ibution of each component with rms errors of about 1 per cent for the CMB, and 10 per cent for the much weaker Galactic components. Radio sources are almost completely recovered down to a flux limit corresponding to similar o r equal to0.7 sigma (CMB), where sigma (CMB) is the rms level of the CMB fl uctuations. The signal recovered has equal quality on all scales larger tha n the pixel size. In addition, we show that for the strongest components (C MB and radio sources) the frequency scaling is recovered with per cent prec ision. Thus, algorithms of the type presented here appear to be very promis ing tools for component separation. On the other hand, we have been dealing here with a highly idealized situation. Work to include instrumental noise , the effect of different resolving powers at different frequencies and a m ore complete and realistic characterization of astrophysical foregrounds is in progress.