Practical wavelet design on the sphere

This paper considers the design of isotropic analysis functions on the sphere which are perfectly limited in the spectral domain and optimally localized in the spatial domain. This is motivated by the need of localized analysis tools in domains where the data is lying on the sphere, e.g. the science of the Cosmic Microwave Background. Our construction is derived from the localized frames introduced by F. Narcowich et al. [F. Narcowich, P. Petrushev, J. Ward, Localized tight frames on spheres, SIAM J. Math. Anal. 38 (2) (2006) 574–594]. The analysis frames are optimized for given applications and compared numerically using various criteria.