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Estimation of linear operators from scattered impulse responses
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | BIGOT, Jérémie | |
| hal.structure.identifier | Département d'Ingénierie des Systèmes Complexes [DISC] | |
| hal.structure.identifier | Institut des Technologies Avancées en sciences du Vivant [ITAV] | |
| dc.contributor.author | ESCANDE, Paul | |
| hal.structure.identifier | Institut de Mathématiques de Toulouse UMR5219 [IMT] | |
| hal.structure.identifier | Institut des Technologies Avancées en sciences du Vivant [ITAV] | |
| dc.contributor.author | WEISS, Pierre | |
| dc.date.accessioned | 2024-04-04T03:07:54Z | |
| dc.date.available | 2024-04-04T03:07:54Z | |
| dc.date.issued | 2019-11 | |
| dc.identifier.issn | 1063-5203 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/193484 | |
| dc.description.abstractEn | We provide a new estimator of integral operators with smooth kernels, obtained from a set of scattered and noisy impulse responses. The proposed approach relies on the formalism of smoothing in reproducing kernel Hilbert spaces and on the choice of an appropriate regularization term that takes the smoothness of the operator into account. It is numerically tractable in very large dimensions. We study the estimator's robustness to noise and analyze its approximation properties with respect to the size and the geometry of the dataset. In addition, we show minimax optimality of the proposed estimator. | |
| dc.language.iso | en | |
| dc.publisher | Elsevier | |
| dc.subject.en | 94A20 | |
| dc.subject.en | 62H12 | |
| dc.subject.en | 65T60 | |
| dc.subject.en | 68W25 | |
| dc.subject.en | 41A25 | |
| dc.subject.en | 41A15 | |
| dc.subject.en | minimax | |
| dc.subject.en | AMS classifications: 47A58 | |
| dc.subject.en | radial basis functions | |
| dc.subject.en | estimator | |
| dc.subject.en | Reproducing Kernel Hilbert Spaces | |
| dc.subject.en | scattered approximation | |
| dc.subject.en | Integral operator | |
| dc.subject.en | convergence rate | |
| dc.subject.en | complexity | |
| dc.subject.en | numerical | |
| dc.title.en | Estimation of linear operators from scattered impulse responses | |
| dc.type | Article de revue | |
| dc.identifier.doi | 10.1016/j.acha.2017.12.002 | |
| dc.subject.hal | Mathématiques [math]/Théorie de l'information et codage [math.IT] | |
| dc.subject.hal | Mathématiques [math]/Analyse numérique [math.NA] | |
| dc.subject.hal | Mathématiques [math]/Statistiques [math.ST] | |
| dc.subject.hal | Sciences de l'ingénieur [physics]/Traitement du signal et de l'image | |
| dc.identifier.arxiv | 1610.04056 | |
| bordeaux.journal | Applied and Computational Harmonic Analysis | |
| bordeaux.page | 730-758 | |
| bordeaux.volume | 47 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.issue | 3 | |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-01380584 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-01380584v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Applied%20and%20Computational%20Harmonic%20Analysis&rft.date=2019-11&rft.volume=47&rft.issue=3&rft.spage=730-758&rft.epage=730-758&rft.eissn=1063-5203&rft.issn=1063-5203&rft.au=BIGOT,%20J%C3%A9r%C3%A9mie&ESCANDE,%20Paul&WEISS,%20Pierre&rft.genre=article |
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