Super-Resolution on the Two-Dimensional Unit Sphere
share
We study the problem of recovering an atomic measure on the unit 2-sphere π^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 π^2 as it was considered by Y. de Castro F. Gamboa and E. CandΓ©s 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.
READ FULL TEXT