Stochastic expansions in an overcomplete wavelet dictionary

F. Abramovich, T. Sapatinas*, B. W. Silverman

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

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 Poisson process model. The relationships between the parameters of the model and the parameters of those Besov spaces within which realizations will fall are investigated. 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.

Original languageEnglish
Pages (from-to)133-144
Number of pages12
JournalProbability Theory and Related Fields
Volume117
Issue number1
DOIs
StatePublished - May 2000

Keywords

  • Besov spaces
  • Continuous wavelet transform
  • Overcomplete wavelet dictionaries
  • Poisson processes

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