  We describe a maximum likelihood regularized beam deconvolution map-making
algorithm for data from high resolution, polarization sensitive instruments,
such as the Planck data set. The resulting algorithm, which we call PReBeaM, is
pixel-free and solves for the map directly in spherical harmonic space,
avoiding pixelization artifacts. While Fourier methods like ours are expected
to work best when applied to smooth, large-scale asymmetric beam systematics
(such as far-side lobe effects) we show that our m-truncated spherical harmonic
representation of the beam results in negligible reconstruction error -- even
for m as small as 4 for a polarized elliptically asymmetric beam. We describe a
hybrid OpenMP/MPI parallelization scheme which allows us to store and
manipulate the time-ordered data from instruments with arbitrary scanning
strategy. Finally, we apply our technique to noisy data and show that it
succeeds in removing visible power spectrum artifacts without generating excess
noise on small scales.
