BeyondPlanck II. CMB map-making through Gibbs sampling

E. Keihänen, A. -S. Suur-Uski, K. J. Andersen, R. Aurlien, R. Banerji, M. Bersanelli, S. Bertocco, M. Brilenkov, M. Carbone, L. P. L. Colombo, H. K. Eriksen, M. K. Foss, C. Franceschet, U. Fuskeland, S. Galeotta, M. Galloway, S. Gerakakis, E. Gjerløw, B. Hensley, D. Herman, M. Iacobellis, M. Ieronymaki, H. T. Ihle, J. B. Jewell, A. Karakci, R. Keskitalo, G. Maggio, D. Maino, M. Maris, A. Mennella, S. Paradiso, B. Partridge, M. Reinecke, T. L. Svalheim, D. Tavagnacco, H. Thommesen, M. Tomasi, D. J. Watts, I. K. Wehus, A. Zacchei

Published 2020-11-11Version 1

We present a Gibbs sampling solution to the map-making problem for CMB measurements, building 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 allows us for the first time to bring the destriping baseline length to a single sample. We apply the Gibbs procedure to simulated Planck 30 GHz data. We find that gaps in the time-ordered data are handled efficiently by filling them with simulated noise as part of the Gibbs process. The Gibbs procedure yields a chain of map samples, from which we may compute the posterior mean as a best-estimate map. The variation in the chain provides information on the correlated residual noise, without 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 total number of iterations. The conceptual advantages of the Gibbs sampling approach lies in statistically well-defined error propagation and systematic error correction, and this methodology forms the conceptual basis for the map-making algorithm employed in the BeyondPlanck framework, which implements the first end-to-end Bayesian analysis pipeline for CMB observations.