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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
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Abstract

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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

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