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High precision cosmology requires analysis of large scale surveys in 3D spherical coordinates, i.e. Fourier-Bessel decomposition. Current methods are insufficient for future data-sets from wide-field cosmology surveys. 3DEX (3D EXpansions) is a public code for fast Fourier-Bessel decomposition of 3D all-sky surveys which takes advantage of HEALPix for the calculation of tangential modes. For surveys with millions of galaxies, computation time is reduced by a factor 4-12 depending on the desired scales and accuracy. The formulation is also suitable for pre-calculations and external storage of the spherical harmonics, which allows for further speed improvements. The 3DEX code can accommodate data with masked regions of missing data. It can be applied not only to cosmological data, but also to 3D data in spherical coordinates in other scientific fields.
Future cosmological surveys will provide 3D large scale structure maps with large sky coverage, for which a 3D Spherical Fourier-Bessel (SFB) analysis 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. We present a new fast Discrete Spherical Fourier-Bessel Transform (DSFBT) based on both a discrete Bessel Transform and the HEALPIX angular pixelisation scheme. We tested the 3D wavelet transform and as a toy-application, applied a denoising algorithm in wavelet space to the Virgo large box cosmological simulations and found we can successfully remove noise without much loss to the large scale structure. The new spherical 3D isotropic wavelet transform, called MRS3D, is ideally suited to analysing and denoising future 3D spherical cosmological surveys; it uses a novel discrete spherical Fourier-Bessel Transform. MRS3D is based on two packages, IDL and Healpix and can be used only if these two packages have been installed.