A sampling theorem on the sphere has been developed recently, requiring half
as many samples as alternative equiangular sampling theorems on the sphere. A
reduction by a factor of two in the number of samples required to represent a
band-limited signal on the sphere exactly has important implications for
compressed 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 the superior reconstruction performance when
adopting the new sampling theorem compared to the alternative.Comment: 1 page, 2 figures, Signal Processing with Adaptive Sparse Structured
Representations (SPARS) 201
