  Pressing questions in cosmology such as the nature of dark matter and dark
energy can be addressed using large galaxy surveys, which measure the
positions, properties and redshifts of galaxies in order to map the large-scale
structure of the Universe. We review the Fourier-Laguerre transform, a novel
transform in 3D spherical coordinates which is based on spherical harmonics
combined with damped Laguerre polynomials and appropriate for analysing galaxy
surveys. We also recall the construction of flaglets, 3D wavelets obtained
through a tiling of the Fourier-Laguerre space, which can be used to extract
scale-dependent, spatially localised features on the ball. We exploit a
sampling theorem to obtain exact Fourier-Laguerre and flaglet transforms, such
that band-limited signals can analysed and reconstructed at floating point
accuracy on a finite number of voxels on the ball. We present a potential
application of the flaglet transform for finding voids in galaxy surveys and
studying the large-scale structure of the Universe.
