Non-parametric foreground subtraction for 21-cm epoch of reionization experiments

Authors: Harker, Geraint; Zaroubi, Saleem¹; Bernardi, Gianni¹; Brentjens, Michiel A.²; de Bruyn, A. G.; Ciardi, Benedetta³; Jelić, Vibor¹; Koopmans, Leon V. E.¹; Labropoulos, Panagiotis¹; Mellema, Garrelt⁴; Offringa, André¹; Pandey, V. N.¹; Schaye, Joop⁵; Thomas, Rajat M.¹; Yatawatta, Sarod¹

Source: Monthly Notices of the Royal Astronomical Society, Volume 397, Number 2, August 2009 , pp. 1138-1152(15)

Publisher: Wiley-Blackwell

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Abstract:

One of the problems facing experiments designed to detect redshifted 21-cm emission from the epoch of reionization (EoR) is the presence of foregrounds which exceed the cosmological signal in intensity by orders of magnitude. While fitting them so that they can be removed, we must be careful to minimize `overfitting', in which we fit away some of the cosmological signal, and `underfitting', in which real features of the foregrounds cannot be captured by the fit, polluting the signal reconstruction. We argue that in principle it would be better to fit the foregrounds non-parametrically - allowing the data to determine their shape - rather than selecting some functional form in advance and then fitting its parameters. Non-parametric fits often suffer from other problems, however. We discuss these before suggesting a non-parametric method, Wp smoothing, which seems to avoid some of them.

After outlining the principles of Wp smoothing, we describe an algorithm used to implement it. Some useful results for implementing an alternative algorithm are given in an appendix. We apply Wp smoothing to a synthetic data cube for the Low Frequency Array (LOFAR) EoR experiment. This cube includes realistic models for the signal, foregrounds, instrumental response and noise. The performance of Wp smoothing, measured by the extent to which it is able to recover the variance of the cosmological signal and to which it avoids the fitting residuals being polluted by leakage of power from the foregrounds, is compared to that of a parametric fit, and to another non-parametric method (smoothing splines). We find that Wp smoothing is superior to smoothing splines for our application, and is competitive with parametric methods even though in the latter case we may choose the functional form of the fit with advance knowledge of the simulated foregrounds. Finally, we discuss how the quality of the fit is affected by the frequency resolution and range, by the characteristics of the cosmological signal and by edge effects.

Keywords: methods: statistical; cosmology: theory; diffuse radiation; radio lines: general

Document Type: Research article

DOI: http://dx.doi.org/10.1111/j.1365-2966.2009.15081.x

Affiliations: 1: Kapteyn Astronomical Institute, University of Groningen, PO Box 800, 9700AV Groningen, the Netherlands 2: ASTRON, Postbus 2, 7990AA Dwingeloo, the Netherlands 3: Max-Planck Institute for Astrophysics, Karl-Schwarzschild-Straße 1, 85748 Garching, Germany 4: Department of Astronomy and Oskar Klein Centre for Cosmoparticle Physics, AlbaNova, Stockholm University, SE-106 91 Stockholm, Sweden 5: Leiden Observatory, Leiden University, PO Box 9513, 2300RA Leiden, the Netherlands

Publication date: 2009-08-01

Non-parametric foreground subtraction for 21-cm epoch of reionization experiments

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