Smoothness Characterization and Stability of Nonlinear and Non-Separable Multi-scale Representations

Basarab Matei (1) , Sylvain Meignen (2) , Anastasia Zakharova (2)

1 LAGA - Laboratoire Analyse, Géométrie et Applications
2 MGMI - Modélisation Géométrique & Multirésolution pour l'Image

The aim of the paper is the construction and the analysis of nonlinear and non-separable multi-scale representations for multivariate functions. The described multi-scale representation is associated with an isotropic dilation matrix. We show that the smoothness of a function can be characterized by the rate of decay of its multi-scale coefficients. We also study the stability of these representations, a key issue in the designing of adaptive algorithms.

Mots clés: Nonlinear Multiscale Representations; Convergence; Stability

Domaines: Analyse numérique [math.NA]

Basarab Matei, Sylvain Meignen, Anastasia Zakharova. Smoothness Characterization and Stability of Nonlinear and Non-Separable Multi-scale Representations. Journal of Approximation Theory, 2011, 163 (11), pp.1707-1728. ⟨10.1016/j.jat.2011.06.009⟩. ⟨hal-00472176v2⟩