The Internal Linear Combination (ILC) component separation method has been extensively used to extract a single component, the CMB, from the WMAP multifrequency data. We generalise the ILC approach for separating other millimetre astrophysical emissi
ons. We construct in particular a multidimensional ILC filter, which can be used, for instance, to estimate the diffuse emission of a complex component originating from multiple correlated emissions, such as the total emission of the Galactic interstellar medium. The performance of such generalised ILC methods, implemented on a needlet frame, is tested on simulations of Planck mission observations, for which we successfully reconstruct a low noise estimate of emission from astrophysical foregrounds with vanishing CMB and SZ contamination.
This paper offers a new point of view on component separation, based on a model of additive components which enjoys a much greater flexibility than more traditional linear component models. This flexibility is needed to process the complex full-sky o
bservations of the CMB expected from the Planck space mission, for which it was developed, but it may also be useful in any context where accurate component separation is needed.
