A hybrid approach to CMB lensing reconstruction on all-sky intensity
  maps
  Based on realistic simulations, we propose an hybrid method to reconstruct
the lensing potential power spectrum, directly on PLANCK-like CMB frequency
maps. It implies using a large galactic mask and dealing with a strong
inhomogeneous noise. For l < 100, we show that a full-sky inpainting method,
already described in a previous work, still allows a minimal variance
reconstruction, with a bias that must be accounted for by a Monte-Carlo method,
but that does not couple to the deflection field. For l>100 we develop a method
based on tiling the cut-sky with local 10x10 degrees overlapping tangent planes
(referred to in the following as "patches"). It requires to solve various
issues concerning their size/position, non-periodic boundaries and irregularly
sampled data after the sphere-to-plane projection. We show how the leading
noise term of the quadratic lensing estimator applied onto an apodized patch
can still be taken directly from the data. To not loose spatial accuracy, we
developed a tool that allows the fast determination of the complex Fourier
series coefficients from a bi-dimensional irregularly sampled dataset, without
performing an interpolation. We show that the multi-patch approach allows the
lensing power spectrum reconstruction with a very small bias, thanks to
avoiding the galactic mask and lowering the noise inhomogeneities, while still
having almost a minimal variance. The data quality can be assessed at each
stage and simple bi-dimensional spectra build, which allows the control of
local systematic errors.
