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Open Access Green as soon as Postprint is submitted to ZB.
Recovery of atomic measures on the unit sphere.
Numer. Funct. Anal. Optim. 43, 755-795 (2022)
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
Keywords
Signal Recovery ; Superresolution On The Sphere ; Tv-minimization
Language
english
Publication Year
2022
HGF-reported in Year
2022
ISSN (print) / ISBN
0163-0563
e-ISSN
1532-2467
Quellenangaben
Volume: 43,
Issue: 7,
Pages: 755-795
Publisher
Taylor & Francis
Reviewing status
Peer reviewed
Institute(s)
Institute of Biological and Medical Imaging (IBMI)
POF-Topic(s)
30205 - Bioengineering and Digital Health
Research field(s)
Enabling and Novel Technologies
PSP Element(s)
G-505595-001
Grants
Helmholtz Association
German Research Foundation (DFG)
German Research Foundation (DFG)
WOS ID
WOS:000792712600001
Scopus ID
85130188136
Erfassungsdatum
2022-07-04