Hostname: page-component-78c5997874-t5tsf Total loading time: 0 Render date: 2024-11-10T17:21:46.882Z Has data issue: false hasContentIssue false
  • English
  • Français

On spin scale-discretised wavelets on the sphere for the analysis of CMB polarisation

Published online by Cambridge University Press:  01 July 2015

Jason D. McEwen ,
Martin Büttner ,
Boris Leistedt ,
Hiranya V. Peiris ,
Pierre Vandergheynst  and
Yves Wiaux
Jason D. McEwen
Affiliation:
Mullard Space Science Laboratory (MSSL), University College London (UCL), Surrey RH5 6NT, UK email: jason.mcewen@ucl.ac.uk
Martin Büttner
Affiliation:
Department of Physics and Astronomy, University College London (UCL), London WC1E 6BT, UK email: martin.buettner.11@ucl.ac.uk, boris.leistedt.11@ucl.ac.uk, h.peiris@ucl.ac.uk
Boris Leistedt
Affiliation:
Department of Physics and Astronomy, University College London (UCL), London WC1E 6BT, UK email: martin.buettner.11@ucl.ac.uk, boris.leistedt.11@ucl.ac.uk, h.peiris@ucl.ac.uk
Hiranya V. Peiris
Affiliation:
Department of Physics and Astronomy, University College London (UCL), London WC1E 6BT, UK email: martin.buettner.11@ucl.ac.uk, boris.leistedt.11@ucl.ac.uk, h.peiris@ucl.ac.uk
Pierre Vandergheynst
Affiliation:
Institute of Electrical Engineering, Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland email: pierre.vandergheynst@epfl.ch
Yves Wiaux
Affiliation:
Institute of Sensors, Signals & Systems, Heriot-Watt University, Edinburgh EH14 4AS, UK email: y.wiaux@hw.ac.uk
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

A new spin wavelet transform on the sphere is proposed to analyse the polarisation of the cosmic microwave background (CMB), a spin ± 2 signal observed on the celestial sphere. The scalar directional scale-discretised wavelet transform on the sphere is extended to analyse signals of arbitrary spin. The resulting spin scale-discretised wavelet transform probes the directional intensity of spin signals. A procedure is presented using this new spin wavelet transform to recover E- and B-mode signals from partial-sky observations of CMB polarisation.

Keywords

cosmology: cosmic microwave backgroundcosmology: observationscosmology: early universemethods: data analysistechniques: image processing
Type
Contributed Papers
Information
Proceedings of the International Astronomical Union , Volume 10 , Symposium S306: Statistical Challenges in 21st Century Cosmology , May 2014 , pp. 64 - 67
Copyright
Copyright © International Astronomical Union 2015 

References

Antoine, & Vandergheynst, 1998, J. Math. Phys. 39 8, 3987Google Scholar
Antoine, & Vandergheynst, 1999, ACHA, 7, 1Google Scholar
Baldi, , Kerkyacharian, , Marinucci, , & Picard, 2009, Ann. Stat., 37 No.3, 1150, arXiv:math/0606599Google Scholar
BICEP2 Collaboration 2014, submitted, arXiv:1403.3985Google Scholar
Bobin, , Starck, , Sureau, , & Basak, 2013, A&A 550 A73,arXiv:1206.1773Google Scholar
Bowyer, , Jaffe, , & Novikov, 2011, arXiv, 1009, arXiv:1101.0520Google Scholar
Bunn, , Zaldarriaga, , Tegmark, , & de Oliveira-Costa, 2003, PRD 67 2, 023501, astro-ph/0207338CrossRefGoogle Scholar
Faÿ, , Guilloux, , Betoule, , Cardoso, , Delabrouille, , & Le Jeune, 2008, PRD 78 8, 083013, arXiv:0807.1113CrossRefGoogle Scholar
Feeney, , Johnson, , Mortlock, , & Peiris, 2011a, Phys. Rev. Lett. 107 071301, 1012.1995CrossRefGoogle Scholar
Feeney, , Johnson, , Mortlock, , & Peiris, 2011b, PRD D84 043507, 1012.3667Google Scholar
Geller, , Hansen, , Marinucci, , Kerkyacharian, , & Picard, 2008, PRD 78 12, 123533, arXiv:0811.2881Google Scholar
Górski, , Hivon, , Banday, , Wandelt, , Hansen, , Reinecke, , & Bartelmann, 2005, ApJ 622 759, astro-ph/0409513Google Scholar
Hanson, , et al. 2013, PRL 111 14, 141301, arXiv:1307.5830CrossRefGoogle Scholar
Kim, 2011, A&A 531 A32, arXiv:1010.2636Google Scholar
Leistedt, , McEwen, , Vandergheynst, , & Wiaux, 2013, A&A 558 A128, 1, arXiv:1211.1680Google Scholar
Lewis, & Challinor, , Turok, 2002, PRD 65 2, 023505, astro-ph/0106536Google Scholar
Marinucci, , et al. 2008, MNRAS 383 539, arXiv:0707.0844Google Scholar
McEwen, , Hobson, , & Lasenby, 2006a, ArXiv, astro-ph/0609159Google Scholar
McEwen, , Hobson, , Lasenby, , Mortlock, , 2005, MNRAS 359 1583, astro-ph/0406604CrossRefGoogle Scholar
McEwen, , Hobson, , Lasenby, , & Mortlock, 2006b, MNRAS 371 L50, astro-ph/0604305Google Scholar
McEwen, , Hobson, , Lasenby, , & Mortlock, 2006c, MNRAS, 369, 1858, astro-ph/0510349CrossRefGoogle Scholar
McEwen, , Hobson, , Lasenby, , & Mortlock, 2008a, MNRAS 388 2, 659, arXiv:0803.2157Google Scholar
McEwen, , Hobson, , Mortlock, , & Lasenby, 2007a, IEEE TSP 55 2, 520, astro-ph/0506308Google Scholar
McEwen, , Vandergheynst, , & Wiaux, 2013, in SPIE Wavelets and Sparsity XV, arXiv:1308.5706Google Scholar
McEwen, , Vielva, , Hobson, , Martínez-González, , & Lasenby, 2007b, MNRAS 373 1211, astro-ph/0602398Google Scholar
McEwen, , Wiaux, , Hobson, , Vandergheynst, , & Lasenby, 2008b, MNRAS 384 4, 1289, arXiv:0704.0626Google Scholar
McEwen, , et al. 2007c, JFAA 13 4, 495, arXiv:0704.3158Google Scholar
Naess, , et al. 2014, ArXiv e-prints, arXiv:1405.5524Google Scholar
Narcowich, , Petrushev, , & Ward, 2006, SIAM J. Math. Anal. 38 2, 574Google Scholar
Pietrobon, , Balbi, , & Marinucci, 2006, PRD 74 4, 043524, astro-ph/0606475Google Scholar
Planck Collaboration I 2013, A&A, in press, arXiv:1303.5062Google Scholar
Planck Collaboration XII 2013, A&A, in press, arXiv:1303.5072Google Scholar
Planck Collaboration XXIII 2013, A&A, in press, arXiv:1303.5083Google Scholar
Planck Collaboration XXIV 2014, A&A, in press, arXiv:1303.5084Google Scholar
Planck Collaboration XXV 2013, A&A, in press, arXiv:1303.5085Google Scholar
Spergel, & Zaldarriaga, 1997, PRL 79 2180, astro-ph/9705182Google Scholar
Starck, , Moudden, , & Bobin, 2009, A&A 497 931, arXiv:0902.0574Google Scholar
Starck, , Moudden, , Abrial, , & Nguyen, 2006, A&A 446 1191, astro-ph/0509883Google Scholar
Vielva, , Martínez-González, , Barreiro, , Sanz, & Cayón, 2004, ApJ 609 22, astro-ph/0310273Google Scholar
Vielva, , Wiaux, , Martínez-González, , & Vandergheynst, 2006, New Astronomy Review 50 880, astro-ph/0609147Google Scholar
Wiaux, , Jacques, & Vandergheynst, 2005, ApJ 632 15, astro-ph/0502486Google Scholar
Wiaux, , Jacques, , Vielva, , & Vandergheynst, 2006, ApJ 652 820, astro-ph/0508516Google Scholar
Wiaux, , McEwen, , Vandergheynst, , & Blanc, 2008, MNRAS 388 2, 770, arXiv:0712.3519Google Scholar
Zaldarriaga, 1997, PRD 55 1822, astro-ph/9608050Google Scholar
Zaldarriaga, & Seljak, 1997, PRD 55 4, 1830, astro-ph/9609170Google Scholar