Super-Resolution on the Two-Dimensional Unit Sphere

07/22/2021

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by   Frank Filbir, et al.

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We study the problem of recovering an atomic measure on the unit 2-sphere 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 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.