Application of beam deconvolution technique to power spectrum estimation
  for CMB measurements
  We present two novel methods for the estimation of the angular power spectrum
of cosmic microwave background (CMB) anisotropies. We assume an absolute CMB
experiment with arbitrary asymmetric beams and arbitrary sky coverage. The
methods differ from earlier ones in that the power spectrum is estimated
directly from time-ordered data, without first compressing the data into a sky
map, and they take into account the effect of asymmetric beams. In particular,
they correct the beam-induced leakage from temperature to polarization. The
methods are applicable to a case where part of the sky has been masked out to
remove foreground contamination, leaving a pure CMB signal, but incomplete sky
coverage. The first method (DQML) is derived as the optimal quadratic
estimator, which simultaneously yields an unbiased spectrum estimate and
minimizes its variance. We successfully apply it to multipoles up to
$\ell$=200. The second method is derived as a weak-signal approximation from
the first one. It yields an unbiased estimate for the full multipole range, but
relaxes the requirement of minimal variance. We validate the methods with
simulations for the 70 GHz channel of {\tt Planck} surveyor, and demonstrate
that we are able to correct the beam effects in the $TT$, $EE$, $BB$, and $TE$
spectra up to multipole $\ell$=1500. Together the two methods cover the
complete multipole range with no gap in between.
