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

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

1 LJK - Laboratoire Jean Kuntzmann
2 LAGA - Laboratoire Analyse, Géométrie et Applications

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]

Sylvain Meignen, Basarab Matei, Anastasia Zakharova. Smoothness Characterization and Stability of Nonlinear and Non-Separable Multi-scale Representations. 2010. ⟨hal-00472176v1⟩