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Stochastic expansions in an overcomplete wavelet dictionary
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  • Published: May 2000

Stochastic expansions in an overcomplete wavelet dictionary

  • F. Abramovich1,
  • T. Sapatinas3 &
  • B.W. Silverman2 

Probability Theory and Related Fields volume 117, pages 133–144 (2000)Cite this article

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  • 13 Citations

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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.

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Authors and Affiliations

  1. Department of Statistics and Operations Research, Raymond & Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Ramat Aviv 69978, Israel, , , , , , IL

    F. Abramovich

  2. School of Mathematics, University of Bristol, Bristol BS8 1TW, United Kingdom, , , , , , GB

    B.W. Silverman

  3. Institute of Mathematics and Statistics, University of Kent at Canterbury, Canterbury, Kent CT2 7NF, United Kingdom. e-mail: T.Sapatinas@ukc.ac.uk, , , , , , GB

    T. Sapatinas

Authors
  1. F. Abramovich
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  2. T. Sapatinas
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  3. B.W. Silverman
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Received: 21 September 1998 / Revised version: 20 August 1999 / Published online: 30 March 2000

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Cite this article

Abramovich, F., Sapatinas, T. & Silverman, B. Stochastic expansions in an overcomplete wavelet dictionary. Probab Theory Relat Fields 117, 133–144 (2000). https://doi.org/10.1007/s004400050268

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  • Issue Date: May 2000

  • DOI: https://doi.org/10.1007/s004400050268

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Keywords

  • Basis Function
  • Poisson Process
  • Bayesian Approach
  • Random Function
  • Besov Space
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