Geometric Wavelet Approximations and Differencing

Abdourrahmane Atto (1) , Emmanuel Trouvé (1) , Jean-Marie Nicolas (2)

1 LISTIC - Laboratoire d'Informatique, Systèmes, Traitement de l'Information et de la Connaissance
2 LTCI - Laboratoire Traitement et Communication de l'Information

The paper introduces the concept of geometric wavelets defined from multiplicative algebras. These wavelets perform generalized geometric approximations and differencing. The paper also highlights the statistical properties of multiplicative observation models when the analysis is performed by using multiplicative wavelet transforms. It shows that multiplicative wavelets are more relevant for the representation of piecewise smooth signals observed in presence of multiplicative noise, the sole case where additive and multiplicative wavelet transforms share the same properties being the case of constant signals.

Mots clés: Wavelets; Geometric convolution; Geometric approximations; Geometric differencing

Domaines: Théorie de l'information et codage [math.IT]; Théorie de l'information [cs.IT]

Abdourrahmane Atto, Emmanuel Trouvé, Jean-Marie Nicolas. Geometric Wavelet Approximations and Differencing. 2014. ⟨hal-00950823v1⟩