2001/06/28 by Benjamin D. Wandelt, B. D. Wandelt, Frode K. Hansen · 1 citation
Engineering · Mathematics · Physics and Astronomy · #Advanced Wireless Communication Techniques #Algorithm #Anisotropy #Artificial intelligence #Astrophysics #Class (philosophy) #Computation #Computer science #Computer vision #Cosmic microwave background #Cosmology and Gravitation Theories #Data set #Geometry #Mathematics #Noise (video) #Optics #Physics #Planck #Radio Astronomy Observations and Technology #Set (abstract data type) #Sky #Spectral density #Statistical physics #Statistics #Torus #astro-ph
paper · pdf · doi:10.1103/physrevd.67.023001
published as Phys.Rev. D67 (2003) 023001 · RevTeX, 14 pages, 5 figures. A full resolution version of Figure 1 and additional materials are at http://feynman.princeton.edu/~bwandelt/RTM
arxiv created 2001/06/28 · openalex publication_date 2003/01/16 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We describe a class of observational strategies for probing the anisotropies in the cosmic microwave background (CMB) where the instrument scans on rings which can be combined into an n-torus, the ring torus. This class has the remarkable property that it allows an exact maximum likelihood power spectrum estimation in operations of order N2 (if the size of the data set is N) under circumstances which would previously have made this analysis intractable: correlated receiver noise, arbitrary asymmetric beam shapes and far side lobes, nonuniform distribution of integration time on the sky, and partial sky coverage. This ease of computation gives us an important theoretical tool for understanding the impact of instrumental effects on CMB observables and hence for the design and analysis of CMB observations in the future. There are members of this class which closely approximate the MAP and Planck satellite missions. We present a numerical example where we apply our ring torus methods to a simulated data set from a CMB mission covering a 20\ifmmode^∘\else\textdegree\fi patch on the sky to compute the maximum likelihood estimate of the power spectrum Cl with unprecedented efficiency.