DOSSAL, Charles; LE PENNEC, Erwan; MALLAT, Stéphane

doi:10.1016/j.sigpro.2011.01.013

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DOSSAL, Charles
Institut de Mathématiques de Bordeaux [IMB]

LE PENNEC, Erwan
Laboratoire de Probabilités et Modèles Aléatoires [LPMA]
Model selection in statistical learning [SELECT]
Laboratoire de Mathématiques d'Orsay [LMO]

MALLAT, Stéphane
Centre de Mathématiques Appliquées de l'Ecole polytechnique [CMAP]

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Article de revue

Ce document a été publié dans

Signal Processing. 2011-01, vol. 91, n° 12, p. 2743-2753

Elsevier

Résumé en anglais

To estimate geometrically regular images in the white noise model and obtain an adaptive near asymptotic minimaxity result, we consider a model selection based bandlet estimator. This bandlet estimator combines the best basis selection behaviour of the model selection and the approximation properties of the bandlet dictionary. We derive its near asymptotic minimaxity for geometrically regular images as an example of model selection with general dictionary of orthogonal bases. This paper is thus also a self contained tutorial on model selection with orthogonal bases dictionary.< Réduire