Blind source separation in the presence of weak source

We investigate the information processing of a linear mixture of independent sources of different magnitudes. In particular we consider the case where a number $m$ of the sources can be considered as ``strong'' as compared to the other ones, the ``weak'' sources. We find that it is preferable to perform blind source separation in the space spanned by the strong sources, and that this can be easily done by first projecting the signal onto the $m$ largest principal components. We illustrate the analytical results with numerical simulations.