F. Lanusse, A. Rassat, J. -L. Starck
Future cosmological surveys will provide 3D large scale structure maps with
large sky coverage, for which a 3D Spherical Fourier-Bessel (SFB) analysis in
is natural. Wavelets are particularly well-suited to the analysis and denoising
of cosmological data, but a spherical 3D isotropic wavelet transform does not
currently exist to analyse spherical 3D data. The aim of this paper is to
present a new formalism for a spherical 3D isotropic wavelet, i.e. one based on
the Fourier-Bessel decomposition of a 3D field and accompany the formalism with
a public code to perform wavelet transforms. We describe a new 3D isotropic
spherical wavelet decomposition based on the undecimated wavelet transform
(UWT) described in Starck et al. 2006. We also present a new fast Discrete
Spherical Fourier-Bessel Transform (DSFBT) based on both a discrete Bessel
Transform and the HEALPIX angular pixelisation scheme. We test the 3D wavelet
transform and as a toy-application, apply a denoising algorithm in wavelet
space to the Virgo large box cosmological simulations and find we can
successfully remove noise without much loss to the large scale structure. We
have described a new spherical 3D isotropic wavelet transform, ideally suited
to analyse and denoise future 3D spherical cosmological surveys, which uses a
novel discrete spherical Fourier-Bessel Transform. We illustrate its potential
use for denoising using a toy model. All the algorithms presented in this paper
are available for download as a public code called MRS3D at
http://jstarck.free.fr/mrs3d.html
View original:
http://arxiv.org/abs/1112.0561
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