Super-Resolution on the Two-Dimensional Unit Sphere

Abstract

We study the problem of recovering an atomic measure on the unit 2-sphere ${\mathbb{S}}^2$ given finitely many moments with respect to spherical harmonics. The analysis relies on the formulation of this problem as an optimization problem on the space of bounded Borel measures on ${\mathbb{S}}^2$ as it was considered by Y. de Castro & F. Gamboa and E. Candés & C. Fernandez-Granda. We construct a dual certificate using a kernel given in an explicit form and make a concrete analysis of the interpolation problem. Numerical examples are provided and analyzed.

58 pages, 17 figures

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• Super-resolution on the Sphere using Convex Optimization
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