Geometric Wavelet Approximations and Differencing
Résumé
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.
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