PReBeaM for Planck: A Polarized Regularized Beam Deconvolution Map-Making Method

TL;DR

PReBeaM is a novel regularized beam deconvolution algorithm for high-resolution polarization data, effectively removing artifacts and handling complex beam systematics directly in spherical harmonic space.

Contribution

It introduces a pixel-free, maximum likelihood regularized map-making method that operates in spherical harmonic space, improving artifact removal and computational efficiency for polarization data.

Findings

Successfully removes power spectrum artifacts from noisy data

Handles complex asymmetric beams with minimal reconstruction error

Operates efficiently with parallel OpenMP/MPI implementation

Abstract

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.