Inversion of noisy Radon transform by SVD based needlets

Gérard Kerkyacharian; George Kyriazis; Erwan Le Pennec; Pencho Petrushev; Dominique Picard

doi:10.1016/j.acha.2009.06.001

Inversion of noisy Radon transform by SVD based needlets

Gérard Kerkyacharian
, George Kyriazis
, Erwan Le Pennec
, Pencho Petrushev
, Dominique Picard

Universite Paris Diderot
Laboratoire de Probabilités et Modèles Aléatoires

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

12 Citations (Scopus)

Résumé

A linear method for inverting noisy observations of the Radon transform is developed based on decomposition systems (needlets) with rapidly decaying elements induced by the Radon transform SVD basis. Upper bounds of the risk of the estimator are established in L^p (1 ≤ p ≤ ∞) norms for functions with Besov space smoothness. A practical implementation of the method is given and several examples are discussed.

langue originale	Anglais
Pages (de - à)	24-45
Nombre de pages	22
journal	Applied and Computational Harmonic Analysis
Volume	28
Numéro de publication	1
Les DOIs	https://doi.org/10.1016/j.acha.2009.06.001
état	Publié - 1 janv. 2010
Modification externe	Oui

Accès au document

10.1016/j.acha.2009.06.001

Contient cette citation

@article{c41953ba473a4fff93602cb59d044100,

title = "Inversion of noisy Radon transform by SVD based needlets",

abstract = "A linear method for inverting noisy observations of the Radon transform is developed based on decomposition systems (needlets) with rapidly decaying elements induced by the Radon transform SVD basis. Upper bounds of the risk of the estimator are established in Lp (1 ≤ p ≤ ∞) norms for functions with Besov space smoothness. A practical implementation of the method is given and several examples are discussed.",

author = "G{\'e}rard Kerkyacharian and George Kyriazis and \{Le Pennec\}, Erwan and Pencho Petrushev and Dominique Picard",

year = "2010",

month = jan,

day = "1",

doi = "10.1016/j.acha.2009.06.001",

language = "English",

volume = "28",

pages = "24--45",

journal = "Applied and Computational Harmonic Analysis",

issn = "1063-5203",

publisher = "Academic Press Inc.",

number = "1",

}

TY - JOUR

T1 - Inversion of noisy Radon transform by SVD based needlets

AU - Kerkyacharian, Gérard

AU - Kyriazis, George

AU - Le Pennec, Erwan

AU - Petrushev, Pencho

AU - Picard, Dominique

PY - 2010/1/1

Y1 - 2010/1/1

N2 - A linear method for inverting noisy observations of the Radon transform is developed based on decomposition systems (needlets) with rapidly decaying elements induced by the Radon transform SVD basis. Upper bounds of the risk of the estimator are established in Lp (1 ≤ p ≤ ∞) norms for functions with Besov space smoothness. A practical implementation of the method is given and several examples are discussed.

AB - A linear method for inverting noisy observations of the Radon transform is developed based on decomposition systems (needlets) with rapidly decaying elements induced by the Radon transform SVD basis. Upper bounds of the risk of the estimator are established in Lp (1 ≤ p ≤ ∞) norms for functions with Besov space smoothness. A practical implementation of the method is given and several examples are discussed.

U2 - 10.1016/j.acha.2009.06.001

DO - 10.1016/j.acha.2009.06.001

M3 - Article

AN - SCOPUS:70350723470

SN - 1063-5203

VL - 28

SP - 24

EP - 45

JO - Applied and Computational Harmonic Analysis

JF - Applied and Computational Harmonic Analysis

IS - 1

ER -

Inversion of noisy Radon transform by SVD based needlets

Résumé

Accès au document

Empreinte digitale

Contient cette citation