Comment on the application of the independent component analysis for the blind source separation of microwave astrophysical backgrounds

In order to separate the microwave astrophysical components superposed in maps of the sky, Maino et al. (2002) apply the Fastica algorithm, which is able to recover emissions from statistically independent processes with the only a priori assumption that all the components, except possibly one, must have non-Gaussian distributions. This comment highlights that Fastica is programmed in order to find orthogonal components, while the microwave astrophysical diffuse emissions cannot be considered, a priori, as orthogonal. Therefore, in this case, whatever blind source component separation technique that is not assuming orthogonality among the sources is expected to be better than Fastica. Merely for purposes of example, one of these possible algorithms is presented and compared with Fastica in a very simple toy model.