Bandlet Image Estimation with Model Selection

Charles H Dossal (1) , Erwan Le Pennec (2) , Stéphane Mallat (3)

1 IMB - Institut de Mathématiques de Bordeaux
2 LPMA - Laboratoire de Probabilités et Modèles Aléatoires
3 CMAP - Centre de Mathématiques Appliquées

A new estimator is introduced to reduce white noise added to images having a geometrical regularity. This estimator projects the observations on orthogonal bandlet vectors selected in a dictionary of orthonormal bases. It is proved that the resulting risk is quasi asymptotically minimax for geometrically regular images. This paper is also a tutorial on estimation with general dictionary of orthogonal bases, through model selection. It explains how to build a thresholding estimator in a adaptively chosen ``best'' basis and gives a simple proof of its performance with the model selection approach of Barron, Birge and Massart

Domaines: Statistiques [math.ST]; Théorie [stat.TH]; Traitement des images [eess.IV]

Charles H Dossal, Erwan Le Pennec, Stéphane Mallat. Bandlet Image Estimation with Model Selection. 2008. ⟨hal-00321965v1⟩