A multivariate generalization of Prony's method
DC Element | Wert | Sprache |
---|---|---|
dc.contributor.author | Kunis, Stefan | |
dc.contributor.author | Peter, Thomas | |
dc.contributor.author | Roemer, Tim | |
dc.contributor.author | von der Ohe, Ulrich | |
dc.date.accessioned | 2021-12-23T16:13:11Z | - |
dc.date.available | 2021-12-23T16:13:11Z | - |
dc.date.issued | 2016 | |
dc.identifier.issn | 00243795 | |
dc.identifier.uri | https://osnascholar.ub.uni-osnabrueck.de/handle/unios/10449 | - |
dc.description.abstract | Prony's method is a prototypical eigenvalue analysis based method for the reconstruction of a finitely supported complex measure on the unit circle from its moments up to a certain degree. In this note, we give a generalization of this method to the multivariate case and prove simple conditions under which the problem admits a unique solution. Provided the order of the moments is bounded from below by the number of points on which the measure is supported as well as by a small constant divided by the separation distance of these points, stable reconstruction is guaranteed. In its simplest form, the reconstruction method consists of setting up a certain multilevel Toeplitz matrix of the moments, compute a basis of its kernel, and compute by some method of choice the set of common roots of the multivariate polynomials whose coefficients are given in the second step. All theoretical results are illustrated by numerical experiments. (C) 2015 Elsevier Inc. All rights reserved. | |
dc.description.sponsorship | DFG within the research training group Combinatorial structures in geometry [GRK-1916]; Helmholtz Association within the young investigator group Fast algorithms for biomedical imaging [VH-NG-526]; The authors thank S. Heider for the implementation of the approach [7] for the bivariate case and H.M. Moller for several enlightening discussions. The fourth author expresses his thanks to J. Abbott for warm hospitality during his visit in Genoa and numerous useful suggestions. Moreover, we gratefully acknowledge support by the DFG within the research training group GRK-1916: Combinatorial structures in geometry and by the Helmholtz Association within the young investigator group VH-NG-526: Fast algorithms for biomedical imaging. | |
dc.language.iso | en | |
dc.publisher | ELSEVIER SCIENCE INC | |
dc.relation.ispartof | LINEAR ALGEBRA AND ITS APPLICATIONS | |
dc.subject | Exponential sum | |
dc.subject | FOURIER | |
dc.subject | Frequency analysis | |
dc.subject | INTERPOLATION | |
dc.subject | Mathematics | |
dc.subject | Mathematics, Applied | |
dc.subject | Moment problem | |
dc.subject | PARAMETER-ESTIMATION | |
dc.subject | RECONSTRUCTION | |
dc.subject | Spectral analysis | |
dc.subject | Super-resolution | |
dc.title | A multivariate generalization of Prony's method | |
dc.type | journal article | |
dc.identifier.doi | 10.1016/j.laa.2015.10.023 | |
dc.identifier.isi | ISI:000370461400003 | |
dc.description.volume | 490 | |
dc.description.startpage | 31 | |
dc.description.endpage | 47 | |
dc.identifier.eissn | 18731856 | |
dc.publisher.place | STE 800, 230 PARK AVE, NEW YORK, NY 10169 USA | |
dcterms.isPartOf.abbreviation | Linear Alg. Appl. | |
dcterms.oaStatus | Green Submitted, Bronze | |
crisitem.author.dept | FB 06 - Mathematik/Informatik | - |
crisitem.author.dept | FB 06 - Mathematik/Informatik | - |
crisitem.author.deptid | fb06 | - |
crisitem.author.deptid | fb06 | - |
crisitem.author.parentorg | Universität Osnabrück | - |
crisitem.author.parentorg | Universität Osnabrück | - |
crisitem.author.netid | KuSt212 | - |
crisitem.author.netid | RoTi119 | - |
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