Department of Mathematics

Applied Mathematics

  •  Anna Veselovska, Department of Mathematics, Technical University of Munich, Germany
  •  Super-Resolution on the Two-Dimensional Unit Sphere
  •  09/16/2022
  •  4:00 PM - 5:00 PM
  •  C304 Wells Hall
  •  Mark A Iwen (iwenmark@msu.edu)

In this talk, we discuss 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 suggested by Y. de Castro & F. Gamboa and E. Candes & 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. We support our theoretical results by various numerical examples related to direct solution of the optimization problem and its discretization. This is a joint work with Frank Filbir and Kristof Schroder.

 

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Department of Mathematics
Michigan State University
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