Exponential decay of scattering coefficients

Irène Waldspurger (1, 2)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
2 MOKAPLAN - Méthodes numériques pour le problème de Monge-Kantorovich et Applications en sciences sociales

The scattering transform is a deep representation, defined as a cascade of wavelet transforms followed by the application of a complex modulus. In her PhD, the author showed that, under some conditions on the wavelets, the norm of the scattering coefficients at a given layer only depends on the values of the signal outside a frequency band whose size is exponential in the depth of the layer. We give here a succinct presentation of this result, and slightly generalize it by removing one of the assumptions on the wavelets (namely the weak analyticity condition).

Domaines: Analyse fonctionnelle [math.FA]

Irène Waldspurger. Exponential decay of scattering coefficients. SampTA 2017 - Sampling Theory and Applications, Jul 2017, Tallinn, Estonia. ⟨hal-01645078v2⟩