Source separation in cosmology, from global to local models

After a series of successful full-sky CMB (Cosmic Microwave Background) experiments (COBE and WMAP to only name two), the latest spatial mission of the European Space Agency, Planck, has started observing the whole sky in mid-2009. This experiment is of premier importance for the cosmologists to study the birth of our universe via the analysis of the CMB. The latter astrophysical component, among others, is not directly observable in the Planck data but rather mixed up with other components. For the sake of scientific exploitation, accessing such precious physical information requires extracting several different astrophysi-cal components (CMB, Sunyaev-Zel´dovich clusters, galactic dust). Mathematically, this problem amounts to a component separation problem. In the field of CMB studies, a very large range of state-of-the art source separation methods have been applied. Most of these methods assume that the sought after components are mixed up in the data according to the standard global linear mixture model. Nevertheless, this model does not hold and more accurate models require modeling the mixtures locally rather than globally. The purpose of this paper is to introduce an extension of GMCA (Generalized Morphological Component Analysis) to handle a local mixture model. Preliminary results on simulated Planck data are presented.