  We discuss a novel sampling theorem on the sphere developed by McEwen & Wiaux
recently through an association between the sphere and the torus. To represent
a band-limited signal exactly, this new sampling theorem requires less than
half the number of samples of other equiangular sampling theorems on the
sphere, such as the canonical Driscoll & Healy sampling theorem. A reduction in
the number of samples required to represent a band-limited signal on the sphere
has important implications for compressive sensing, both in terms of the
dimensionality and sparsity of signals. We illustrate the impact of this
property with an inpainting problem on the sphere, where we show superior
reconstruction performance when adopting the new sampling theorem.
