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 (CMB) radiation, as performed by the Wilkinson Microwave Anisotropy Probe satellite and the more recent Planck mission, launched on 2009 May 14 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 CMB 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 (less than 1 per cent) with a Planck-style mission, the ILC method can lead to inaccurate CMB reconstruction in the high signal-to-noise ratio 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.
