  We study the impact of sampling theorems on the fidelity of sparse image
reconstruction on the sphere. We discuss how a reduction in the number of
samples required to represent all information content of a band-limited signal
acts to improve the fidelity of sparse image reconstruction, through both the
dimensionality and sparsity of signals. To demonstrate this result we consider
a simple inpainting problem on the sphere and consider images sparse in the
magnitude of their gradient. We develop a framework for total variation (TV)
inpainting on the sphere, including fast methods to render the inpainting
problem computationally feasible at high-resolution. Recently a new sampling
theorem on the sphere was developed, reducing the required number of samples by
a factor of two for equiangular sampling schemes. Through numerical simulations
we verify the enhanced fidelity of sparse image reconstruction due to the more
efficient sampling of the sphere provided by the new sampling theorem.
