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.