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Filbir, F. ; Schroeder, K.* ; Veselovska, A.*

Recovery of atomic measures on the unit sphere.

Numer. Funct. Anal. Optim. 43, 755-795 (2022)
DOI
Open Access Green as soon as Postprint is submitted to ZB.
We study the problem of recovering an atomic measure on the unit 2-sphere (Formula presented.) 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 (Formula presented.) 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.
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Publication type Article: Journal article
Document type Scientific Article
Corresponding Author
Keywords Signal Recovery ; Superresolution On The Sphere ; Tv-minimization
ISSN (print) / ISBN 0163-0563
e-ISSN 1532-2467
Journal Numerical Functional Analysis and Optimization
Quellenangaben Volume: 43, Issue: 7, Pages: 755-795 Article Number: , Supplement: ,
Publisher Taylor & Francis
Non-patent literature Publications
Reviewing status Peer reviewed
Institute(s) Institute of Biological and Medical Imaging (IBMI)
Grants Helmholtz Association
German Research Foundation (DFG)