Non-uniform spline recovery from small degree polynomial approximation - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Journal of Mathematical Analysis and Applications Année : 2015

Non-uniform spline recovery from small degree polynomial approximation

Résumé

We investigate the sparse spikes deconvolution problem onto spaces of algebraic polynomials. Our framework encompasses the measure reconstruction problem from a combination of noiseless and noisy moment measurements. We study a TV-norm regularization procedure to localize the support and estimate the weights of a target discrete measure in this frame. Furthermore, we derive quantitative bounds on the support recovery and the amplitudes errors under a Chebyshev-type minimal separation condition on its support. Incidentally, we study the localization of the knots of non-uniform splines when a Gaussian perturbation of their inner-products with a known polynomial basis is observed (i.e. a small degree polynomial approximation is known) and the boundary conditions are known. We prove that the knots can be recovered in a grid-free manner using semidefinite programming.
Fichier principal
Vignette du fichier
JMAA_DECASTRO_MIJOULE_R3.pdf (809.3 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-00950850 , version 1 (23-02-2014)
hal-00950850 , version 2 (25-05-2015)

Licence

Paternité - Pas d'utilisation commerciale

Identifiants

Citer

Yohann de Castro, Guillaume Mijoule. Non-uniform spline recovery from small degree polynomial approximation. Journal of Mathematical Analysis and Applications, 2015, 430 (2), ⟨10.1016/j.jmaa.2015.05.034⟩. ⟨hal-00950850v2⟩
236 Consultations
143 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More