Multidimensional ICA and its performance analysis applied to CMB observations

This paper deals with multidimensional ICA and its performance analysis, applied to cosmological observations. Our purpose is the separation of the cosmic microwave background radiation from the Galactic emission, in a noise-free setup, using a model of correlated sources. Since the Galactic emission does not obey this model, we propose a method to select the effective model order. As there are more detectors than signal-space dimensions, a dimension reduction scheme is derived. Our simulations show a good match between the closed-form analytical expression for the error and its empirical counterpart. This analytical expression is compact and involves inversions only of small matrices. Therefore, it can serve as a reliable predictor of the separation error without resorting to exhaustive Monte-Carlo trials.