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We consider random functions defined in terms of members of an overcomplete wavelet dictionary. The function is modelled as a sum of wavelet components at arbitrary positions and scales where the locations of the wavelet components and the magnitudes of their coefficients are chosen with respect to a marked Pois- son process model. The relationships between the parameters of the model and the parameters of those Besov spaces within which realizations will fall are in- vestigated. The models allow functions with specified regularity properties to be generated. They can potentially be used as priors in a Bayesian approach to curve estimation, extending current standard wavelet methods to be free from the dyadic positions and scales of the basis functions.

Stochastic expansions in an overcomplete wavelet dictionary