Sparse component separation for accurate cosmic microwave background estimation

The cosmic microwave background (CMB) is of premier importance for cosmologists in studying the birth of our universe. Unfortunately, most CMB experiments, such as COBE, WMAP, or Planck do not directly measure the cosmological signal, because the CMB is mixed up with galactic foregrounds and point sources. For the sake of scientific exploitation, measuring the CMB requires extracting several different astrophysical components (CMB, Sunyaev-Zel'dovich clusters, galactic dust) from multiwavelength observations. Mathematically speaking, the problem of disentangling the CMB map from the galactic foregrounds amounts to a component or source separation problem. In the field of CMB studies, a wide range of source separation methods have been applied that all differ in the way they model the data and in the criteria they rely on to separate components. Two main difficulties are i) that the instrument's beam varies across frequencies and ii) that the emission laws of most astrophysical components vary across pixels. This paper aims at introducing a very accurate modeling of CMB data, based on sparsity to account for beams' variability across frequencies, as well as for spatial variations of the components' spectral characteristics. Based on this new sparse modeling of the data, a sparsity-based component separation method coined local-generalized morphological component analysis (L-GMCA) is described. Extensive numerical experiments have been carried out with simulated Planck data. These experiments show the high efficiency of the proposed component separation methods for estimating a clean CMB map with a very low foreground contamination, which makes L-GMCA of prime interest for CMB studies.