Low-l CMB analysis and inpainting

Reconstructing the cosmic microwave background (CMB) in the Galactic plane is extremely difficult due to the dominant foreground emissions such as dust, free-free or synchrotron. For cosmological studies, the standard approach consists in masking this area where the reconstruction is insufficient. This leads to difficulties for the statistical analysis of the CMB map, especially at very large scales (to study for instance the low quadrupole, integrated Sachs Wolfe effect, axis of evil, etc.). We investigate how well some inpainting techniques can recover the low-l spherical harmonic coefficients. We introduce three new inpainting techniques based on three different kinds of priors: sparsity, energy, and isotropy, which we compare. We show that sparsity and energy priors can lead to extremely high-quality reconstruction, within 1% of the cosmic variance for a mask with a sky coverage larger than 80%.