0326-Low-$\ell$ CMB analysis and inpainting Starck 2013

Low-$\ell$ CMB analysis and inpainting Starck 2013

the sparsity prior on a signal consists of assuming that its coefficients in a given representation domain, when sorted in decreasing order of magnitude, exhibit a fast decay rate, typically a polynomial decay with an exponent that depends on the regularity of the signal. Spherical harmonic coefficients of the CMB show a decay in O(−2) up to around 900 and then O(−3) for larger multipoles.

diffuse inpainting

A slightly more sophisticated method consists of replacing each missing pixel by the average of its neighbors and iterating until the gaps are filled. This technique is called diffuse inpainting and has been used in Planck-LFI data pre-processing

It is acceptable for treatment of point sources, but is far from being a reasonable solution for the Galactic plane inpainting in a CMB non-Gaussianity analysis.