Volume 549, January 2013
|Number of page(s)||5|
|Published online||08 January 2013|
Efficient Wiener filtering without preconditioning
Institut d’Astrophysique de Paris, UMR 7095, CNRS, Université Paris 6 –
Pierre et Marie Curie
98bis Bd Arago,
2 Departments of Physics and Astronomy, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA
Received: 18 October 2012
Accepted: 20 November 2012
We present a new approach to calculate the Wiener filter solution of general data sets. It is trivial to implement, flexible, numerically absolutely stable, and guaranteed to converge. Most importantly, it does not require an ingenious choice of preconditioner to work well. The method is capable of taking into account inhomogeneous noise distributions and arbitrary mask geometries. It iteratively builds up the signal reconstruction by means of a messenger field, introduced to mediate between the different preferred bases in which signal and noise properties can be specified most conveniently. Using cosmic microwave background (CMB) radiation data as a showcase, we demonstrate the capabilities of our scheme by computing Wiener filtered WMAP7 temperature and polarization maps at full resolution for the first time. We show how the algorithm can be modified to synthesize fluctuation maps, which, combined with the Wiener filter solution, result in unbiased constrained signal realizations, consistent with the observations. The algorithm performs well even on simulated CMB maps with Planck resolution and dynamic range.
Key words: methods: data analysis / methods: statistical / cosmic background radiation
© ESO, 2013
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