A theory of optimal convex regularization for low-dimensional recovery
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | TRAONMILIN, Yann | |
| hal.structure.identifier | Réseaux dynamiques : approche structurelle et temporelle [DANTE] | |
| dc.contributor.author | GRIBONVAL, Rémi | |
| hal.structure.identifier | Laboratoire Jean Alexandre Dieudonné [LJAD] | |
| dc.contributor.author | VAITER, Samuel | |
| dc.date.accessioned | 2024-04-04T02:37:14Z | |
| dc.date.available | 2024-04-04T02:37:14Z | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/190788 | |
| dc.description.abstractEn | We consider the problem of recovering elements of a low-dimensional model from under-determined linear measurements. To perform recovery, we consider the minimization of a convex regularizer subject to a data fit constraint. Given a model, we ask ourselves what is the ``best'' convex regularizer to perform its recovery. To answer this question, we define an optimal regularizer as a function that maximizes a compliance measure with respect to the model. We introduce and study several notions of compliance. We give analytical expressions for compliance measures based on the best-known recovery guarantees with the restricted isometry property. These expressions permit to show the optimality of the ℓ1-norm for sparse recovery and of the nuclear norm for low-rank matrix recovery for these compliance measures. We also investigate the construction of an optimal convex regularizer using the examples of sparsity in levels and of sparse plus low-rank models. | |
| dc.description.sponsorship | Régularisation performante de problèmes inverses en grande dimension pour le traitement de données - ANR-20-CE40-0001 | |
| dc.description.sponsorship | Méthodes variationnelles pour les signaux sur graphe - ANR-18-CE40-0005 | |
| dc.description.sponsorship | Algorithmes, Approximations, Parcimonie et Plongements pour l'IA - ANR-19-CHIA-0009 | |
| dc.language.iso | en | |
| dc.title.en | A theory of optimal convex regularization for low-dimensional recovery | |
| dc.type | Document de travail - Pré-publication | |
| dc.subject.hal | Informatique [cs]/Traitement du signal et de l'image | |
| dc.identifier.arxiv | 2112.03540 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| hal.identifier | hal-03467123 | |
| hal.version | 1 | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-03467123v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.au=TRAONMILIN,%20Yann&GRIBONVAL,%20R%C3%A9mi&VAITER,%20Samuel&rft.genre=preprint |
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