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.

Proceedings of Wavelets and Sparsity XV, SPIE Optics and Photonics 2013