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A sampling theorem on the sphere has been developed recently, requiring halfas many samples as alternative equiangular sampling theorems on the sphere. Areduction by a factor of two in the number of samples required to represent aband-limited signal on the sphere exactly has important implications forcompressed sensing, both in terms of the dimensionality and sparsity ofsignals. We illustrate the impact of this property with an inpainting problemon the sphere, where we show the superior reconstruction performance whenadopting the new sampling theorem compared to the alternative.

Implications for compressed sensing of a new sampling theorem on the sphere