Recovery of Atomic Measures on the Unit Sphere. (19th May 2022)

• Record Type: Journal Article
• Authors: Filbir, Frank; Schröder, Kristof; Veselovska, Anna
• Is Part Of: Numerical functional analysis and optimization. Volume 43:Number 7(2022)
• Page Start: 755
• Page End: 795
• Publication Date: 2022-05-19
• Subjects: Signal recovery -- super-resolution on the sphere -- TV-minimization; Primary: xxxx -- Secondary: yyyy; 00A69; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2022.2052319
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: 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 ( J. Math. Anal. Appl. 395(1):336–354, 2012) and E. Candés & C. Fernandez-Granda ( J. Fourier Anal. Appl. 19(6):1229–1254, 2013). 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.