The statistics of the temperature anisotropies in the primordial Cosmic Microwave Background radiation field provide a wealth of information for cosmology and the estimation of cosmological parameters. An even more acute inference should stem from the study of maps of the polarization state of the CMB radiation. Measuring the latter extremely weak CMB polarization signal requires very sensitive instruments. The full-sky maps of both temperature and polarization anisotropies of the CMB to be delivered by the upcoming Planck Surveyor satellite experiment are hence awaited with excitement. Still, analyzing CMB data requires tackling a number of practical difficulties, notably that several other astrophysical sources emit radiation in the frequency range of CMB observations. Separating the different astrophysical foreground components and the CMB proper from available multichannel data is a problem that has drawn much attention in the community. Nevertheless, some level of residual contributions, most significantly in the galactic region and at the locations of strong radio point sources will unavoidably contaminate the estimated spherical CMB map. Masking out these regions is common practice but the gaps in the data need proper handling. In order to restore the stationarity of a partly incomplete CMB map and thus lower the impact of the gaps on non-local statistical tests, we developed an inpainting algorithm on the sphere to fill in the gaps, based on an iterative thresholding scheme in a sparse representation of the data. This algorithm relies on the variety of recently developed transforms on the sphere among which several multiscale transforms which we will review. We also contribute to enlarging the set of available transforms for polarized data on the sphere. We describe new multiscale decompositions namely the isotropic undecimated wavelet and curvelet transforms for polarized data on the sphere. The proposed transforms are invertible and so allow for applications in image restoration and denoising.

Date Published: 20 September 2007
PDF: 15 pages
Proc. SPIE 6701, Wavelets XII, 670116 (20 September 2007); doi: 10.1117/12.734616

Published in SPIE Proceedings Vol. 6701:
Wavelets XII
Dimitri Van De Ville; Vivek K. Goyal; Manos Papadakis, Editor(s)