  Estimating the cosmological microwave background is of utmost importance for
cosmology. However, its estimation from full-sky surveys such as WMAP or more
recently Planck is challenging: CMB maps are generally estimated via the
application of some source separation techniques which never prevent the final
map from being contaminated with noise and foreground residuals. These spurious
contaminations whether noise or foreground residuals are well-known to be a
plague for most cosmologically relevant tests or evaluations; this includes CMB
lensing reconstruction or non-Gaussian signatures search. Noise reduction is
generally performed by applying a simple Wiener filter in spherical harmonics;
however this does not account for the non-stationarity of the noise. Foreground
contamination is usually tackled by masking the most intense residuals detected
in the map, which makes CMB evaluation harder to perform. In this paper, we
introduce a novel noise reduction framework coined LIW-Filtering for Linear
Iterative Wavelet Filtering which is able to account for the noise spatial
variability thanks to a wavelet-based modeling while keeping the highly desired
linearity of the Wiener filter. We further show that the same filtering
technique can effectively perform foreground contamination reduction thus
providing a globally cleaner CMB map. Numerical results on simulated but
realistic Planck data are provided.
