The basins of attraction of the global minimizers of non-convex inverse problems with low-dimensional models in infinite dimension
| 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 | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | LECLAIRE, Arthur | |
| dc.date.accessioned | 2024-04-04T02:42:16Z | |
| dc.date.available | 2024-04-04T02:42:16Z | |
| dc.date.issued | 2022 | |
| dc.identifier.issn | 2049-8764 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/191229 | |
| dc.description.abstractEn | Non-convex methods for linear inverse problems with low-dimensional models have emerged as an alternative to convex techniques. We propose a theoretical framework where both finite dimensional and infinite dimensional linear inverse problems can be studied. We show how the size of the the basins of attraction of the minimizers of such problems is linked with the number of available measurements. This framework recovers known results about low-rank matrix estimation and off-the-grid sparse spike estimation, and it provides new results for Gaussian mixture estimation from linear measurements. keywords: low-dimensional models, non-convex methods, low-rank matrix recovery, off-the-grid sparse recovery, Gaussian mixture model estimation from linear measurements. | |
| dc.description.sponsorship | Super-résolution d'images multi-échelles en sciences des matériaux avec des attributs géométriques - ANR-18-CE92-0050 | |
| dc.description.sponsorship | Régularisation performante de problèmes inverses en grande dimension pour le traitement de données - ANR-20-CE40-0001 | |
| dc.language.iso | en | |
| dc.publisher | Oxford University Press (OUP) | |
| dc.title.en | The basins of attraction of the global minimizers of non-convex inverse problems with low-dimensional models in infinite dimension | |
| dc.type | Article de revue | |
| 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 | 2009.08670 | |
| bordeaux.journal | Information and Inference | |
| 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-02941814 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-02941814v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Information%20and%20Inference&rft.date=2022&rft.eissn=2049-8764&rft.issn=2049-8764&rft.au=TRAONMILIN,%20Yann&AUJOL,%20Jean-Fran%C3%A7ois&LECLAIRE,%20Arthur&rft.genre=article |
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