The basins of attraction of the global minimizers of the non-convex sparse spike estimation problem
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | TRAONMILIN, Yann | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | AUJOL, Jean-François | |
| dc.date.accessioned | 2024-04-04T02:59:59Z | |
| dc.date.available | 2024-04-04T02:59:59Z | |
| dc.date.issued | 2020-02-21 | |
| dc.identifier.issn | 0266-5611 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/192786 | |
| dc.description.abstractEn | The sparse spike estimation problem consists in estimating a number of off-the-grid impulsive sources from under-determined linear measurements. Information theoretic results ensure that the minimization of a non-convex functional is able to recover the spikes for adequately chosen measurements (deterministic or random). To solve this problem, methods inspired from the case of finite dimensional sparse estimation where a convex program is used have been proposed. Also greedy heuristics have shown nice practical results. However, little is known on the ideal non-convex minimization method. In this article, we study the shape of the global minimum of this non-convex functional: we give an explicit basin of attraction of the global minimum that shows that the non-convex problem becomes easier as the number of measurements grows. This has important consequences for methods involving descent algorithms (such as the greedy heuristic) and it gives insights for potential improvements of such descent methods. | |
| dc.language.iso | en | |
| dc.publisher | IOP Publishing | |
| dc.title.en | The basins of attraction of the global minimizers of the non-convex sparse spike estimation problem | |
| dc.type | Article de revue | |
| dc.identifier.doi | 10.1088/1361-6420/ab5aa3 | |
| dc.subject.hal | Informatique [cs]/Théorie de l'information [cs.IT] | |
| dc.subject.hal | Informatique [cs]/Traitement du signal et de l'image | |
| dc.identifier.arxiv | 1811.12000 | |
| bordeaux.journal | Inverse Problems | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-01938239 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-01938239v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Inverse%20Problems&rft.date=2020-02-21&rft.eissn=0266-5611&rft.issn=0266-5611&rft.au=TRAONMILIN,%20Yann&AUJOL,%20Jean-Fran%C3%A7ois&rft.genre=article |
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