M-band filtering and nonredundant directional wavelets

Sylvain Durand (1)

1 LAMFA - Laboratoire Amiénois de Mathématique Fondamentale et Appliquée

This article introduces families of nonadaptative directional wavelets. Unlike curvelets and contourlets, they are nonredundant and form orthonornal bases for $L^2(\RR^2)$. Their implementation derives from a single nonseparable filter bank structure with nonuniform sampling. We give several examples of frequency partitioning, including construction based on separable multiresolution analyses. We show how to obtain orthonormal bases of wavelets with fast decay and compactly supported, biorthogonal wavelet bases. Some aliasing phenomena that can occur in these construction are discussed.

Mots clés: wavelets; filter banks; image processing

Domaines: Traitement du signal et de l'image [eess.SP]; Traitement du signal et de l'image [eess.SP]

Sylvain Durand. M-band filtering and nonredundant directional wavelets. Applied and Computational Harmonic Analysis, 2007, 22 (1), pp.124-139. ⟨hal-00204978⟩