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

TL;DR

This paper introduces a new sampling theorem on the sphere that reduces the number of samples needed for exact representation of band-limited signals, significantly impacting compressed sensing applications.

Contribution

It presents a novel sampling theorem on the sphere that halves the sample count compared to previous methods, enhancing compressed sensing efficiency.

Findings

Superior reconstruction performance in spherical inpainting using the new sampling theorem

Reduced dimensionality and increased sparsity in signal representation

Implications for more efficient compressed sensing on spherical domains

Abstract

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.