Abstract
In this work, we consider the problem of recovering an ensemble of Diracs on the sphere from its projection onto spaces of spherical harmonics. We show that under an appropriate separation condition on the unknown locations of the Diracs, the ensemble can be recovered through total variation norm minimization. The proof of the uniqueness of the solution uses the method of ‘dual’ interpolating polynomials and is based on Candès and Fernandez-Granda (Commun Pure Appl Math 67:906–956, 2014), where the theory was developed for trigonometric polynomials. We also show that in the special case of nonnegative ensembles, a sparsity condition is sufficient for exact recovery.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
