  The separation of emissions from different astrophysical processes is an
important step towards the understanding of observational data. This topic of
component separation is of particular importance in the observation of the
relic Cosmic Microwave Background Radiation, as performed by the WMAP satellite
and the more recent Planck mission, launched May 14th, 2009 from Kourou and
currently taking data. When performing any sort of component separation, some
assumptions about the components must be used. One assumption that many
techniques typically use is knowledge of the frequency scaling of one or more
components. This assumption may be broken in the presence of calibration
errors. Here we compare, in the context of imperfect calibration, the recovery
of a clean map of emission of the Cosmic Microwave Background from
observational data with two methods: FastICA (which makes no assumption of the
frequency scaling of the components), and an `Internal Linear Combination'
(ILC), which explicitly extracts a component with a given frequency scaling. We
find that even in the presence of small calibration errors with a Planck-style
mission, the ILC method can lead to inaccurate CMB reconstruction in the high
signal-to-noise regime, because of partial cancellation of the CMB emission in
the recovered map. While there is no indication that the failure of the ILC
will translate to other foreground cleaning or component separation techniques,
we propose that all methods which assume knowledge of the frequency scaling of
one or more components be careful to estimate the effects of calibration
errors.
