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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 möglich sobald Postprint bei der ZB eingereicht worden ist.
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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Publikationstyp Artikel: Journalartikel
Dokumenttyp Wissenschaftlicher Artikel
Korrespondenzautor
Schlagwörter Signal Recovery ; Superresolution On The Sphere ; Tv-minimization
ISSN (print) / ISBN 0163-0563
e-ISSN 1532-2467
Zeitschrift Numerical Functional Analysis and Optimization
Quellenangaben Band: 43, Heft: 7, Seiten: 755-795 Artikelnummer: , Supplement: ,
Verlag Taylor & Francis
Nichtpatentliteratur Publikationen
Begutachtungsstatus Peer reviewed
Institut(e) Institute of Biological and Medical Imaging (IBMI)
Förderungen Helmholtz Association
German Research Foundation (DFG)