Journal Article

Maximum likelihood algorithm for parametric component separation in cosmic microwave background experiments

Radek Stompor, Samuel Leach, Federico Stivoli and Carlo Baccigalupi

in Monthly Notices of the Royal Astronomical Society

Published on behalf of The Royal Astronomical Society

Volume 392, issue 1, pages 216-232
Published in print January 2009 | ISSN: 0035-8711
Published online December 2008 | e-ISSN: 1365-2966 | DOI:
Maximum likelihood algorithm for parametric component separation in cosmic microwave background experiments

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We discuss an approach to the component separation of microwave, multifrequency sky maps as those typically produced from cosmic microwave background (CMB) anisotropy data sets. The algorithm is based on the two-step, parametric, likelihood-based technique recently elaborated on by Eriksen et al., where the foreground spectral parameters are estimated prior to the actual separation of the components. In contrast with the previous approaches, we accomplish the former task with help of an analytically derived likelihood function for the spectral parameters, which, we show, yields estimates equal to the maximum likelihood values of the full multidimensional data problem. We then use these estimates to perform the second step via the standard, generalized-least-squares-like procedure. We demonstrate that the proposed approach is equivalent to a direct maximization of the full data likelihood, which is recast in a computationally tractable form. We use the corresponding curvature matrices to characterize statistical properties of the recovered parameters. We incorporate in the formalism some of the essential features of the CMB data sets, such as inhomogeneous pixel domain noise, unknown map offsets as well as calibration errors and study their consequences for the separation. We find that the calibration is likely to have a dominant effect on the precision of the spectral parameter determination for a realistic CMB experiment. We apply the algorithm to simulated data and discuss the results. Our focus is on partial sky, total intensity and polarization, CMB experiments such as planned balloon-borne and ground-based efforts, however, the techniques presented here should be also applicable to the full-sky data as for instance, those produced by the Wilkinson Microwave Anisotropy Probe (WMAP) satellite and anticipated from the Planck mission.

Keywords: methods: data analysis; cosmic microwave background; diffuse radiation

Journal Article.  12068 words.  Illustrated.

Subjects: Astronomy and Astrophysics

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