BEYONDPLANCK

II. CMB mapmaking through Gibbs sampling

¹ Department of Physics, University of Helsinki, Gustaf Hällströmin katu 2, Helsinki, Finland
e-mail: elina.keihanen@helsinki.fi
² Helsinki Institute of Physics, University of Helsinki, Gustaf Hällströmin katu 2, Helsinki, Finland
³ Institute of Theoretical Astrophysics, University of Oslo, Blindern, Oslo, Norway
⁴ Dipartimento di Fisica, Università degli Studi di Milano, Via Celoria, 16, Milano, Italy
⁵ INAF-IASF Milano, Via E. Bassini 15, Milano, Italy
⁶ INFN, Sezione di Milano, Via Celoria 16, Milano, Italy
⁷ INAF – Osservatorio Astronomico di Trieste, Via G. B. Tiepolo 11, Trieste, Italy
⁸ Planetek Hellas, Leoforos Kifisias 44, Marousi 151 25, Greece
⁹ Department of Astrophysical Sciences, Princeton University, Princeton, NJ, 08544, USA
¹⁰ Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, CA, USA
¹¹ Computational Cosmology Center, Lawrence Berkeley National Laboratory, Berkeley, CA, USA
¹² Haverford College Astronomy Department, 370 Lancaster Avenue, Haverford, PA, USA
¹³ Max-Planck-Institut für Astrophysik, Karl-Schwarzschild-Str. 1, 85741 Garching, Germany
¹⁴ Dipartimento di Fisica, Università degli Studi di Trieste, Via A. Valerio 2, Trieste, Italy

Received: 1 December 2021
Accepted: 19 March 2022

Abstract

We present a Gibbs sampling solution to the mapmaking problem for cosmic microwave background (CMB) measurements that builds on existing destriping methodology. Gibbs sampling breaks the computationally heavy destriping problem into two separate steps: noise filtering and map binning. Considered as two separate steps, both are computationally much cheaper than solving the combined problem. This provides a huge performance benefit as compared to traditional methods and it allows us, for the first time, to bring the destriping baseline length to a single sample. Here, we applied the Gibbs procedure to simulated Planck 30 GHz data. We find that gaps in the time-ordered data are handled efficiently by filling them in with simulated noise as part of the Gibbs process. The Gibbs procedure yields a chain of map samples, from which we are able to compute the posterior mean as a best-estimate map. The variation in the chain provides information on the correlated residual noise, without the need to construct a full noise covariance matrix. However, if only a single maximum-likelihood frequency map estimate is required, we find that traditional conjugate gradient solvers converge much faster than a Gibbs sampler in terms of the total number of iterations. The conceptual advantages of the Gibbs sampling approach lies in statistically well-defined error propagation and systematic error correction. This methodology thus forms the conceptual basis for the mapmaking algorithm employed in the BEYONDPLANCK framework, which implements the first end-to-end Bayesian analysis pipeline for CMB observations.