  The polarization modes of the cosmological microwave background are an
invaluable source of information for cosmology, and a unique window to probe
the energy scale of inflation. Extracting such information from microwave
surveys requires disentangling between foreground emissions and the
cosmological signal, which boils down to solving a component separation
problem. Component separation techniques have been widely studied for the
recovery of CMB temperature anisotropies but quite rarely for the polarization
modes. In this case, most component separation techniques make use of
second-order statistics to discriminate between the various components. More
recent methods, which rather emphasize on the sparsity of the components in the
wavelet domain, have been shown to provide low-foreground, full-sky estimate of
the CMB temperature anisotropies. Building on sparsity, the present paper
introduces a new component separation technique dubbed PolGMCA (Polarized
Generalized Morphological Component Analysis), which refines previous work to
specifically tackle the estimation of the polarized CMB maps: i) it benefits
from a recently introduced sparsity-based mechanism to cope with partially
correlated components, ii) it builds upon estimator aggregation techniques to
further yield a better noise contamination/non-Gaussian foreground residual
trade-off. The PolGMCA algorithm is evaluated on simulations of full-sky
polarized microwave sky simulations using the Planck Sky Model (PSM), which
show that the proposed method achieve a precise recovery of the CMB map in
polarization with low noise/foreground contamination residuals. It provides
improvements with respect to standard methods, especially on the galactic
center where estimating the CMB is challenging.
