  Deep surveys of the CMB polarization have more information on the lensing
signal than the quadratic estimators (QE) can capture. We showed in a recent
work that a CMB lensing power spectrum built from a single optimized CMB
lensing mass map, working in close analogy to state-of-the-art QE techniques,
can result in an essentially optimal spectrum estimator at reasonable numerical
cost. We extend this analysis here to account for real-life non-idealities
including masking and realistic instrumental noise maps. As in the QE case, it
is necessary to include small corrections to account for the estimator response
to these anisotropies, which we demonstrate can be estimated easily from
simulations. The realization-dependent debiasing of the spectrum remains
robust, allowing unbiased recovery of the band powers even in cases where the
statistical model used for the lensing map reconstruction is grossly wrong.
This allows now robust and at the same time optimal CMB lensing constraints
from CMB data, on all scales relevant for the inference of the neutrino mass,
or other parameters of our cosmological model.

Cosmology and Nongalactic Astrophysics