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Bayesian Inference in Wavelet-Based Models pp 155–172Cite as

Best Basis Representations with Prior Statistical Models

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Part of the book series: Lecture Notes in Statistics ((LNS,volume 141))

Abstract

Wavelet packets and local trigonometric bases provide an efficient framework and fast algorithms to obtain a “best representation” of a deterministic signal. Applying these deterministic search techniques to stochastic signals may, however, lead to statistically unreliable results. In this chapter, we revisit this problem and introduce prior models on the underlying signal in noise. We propose several techniques to derive the prior parameters and develop a Bayesian-based approach to the best basis problem. As illustrated by applications to signal denoising, this leads to reduced estimation errors while preserving the classical tree search algorithm.

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Authors
  1. David Leporini
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  2. Jean-Christophe Pesquet
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  3. Hamid Krim
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Editor information

Editors and Affiliations

  1. Institute of Statistics and Decision Sciences, Duke University, Box 90251, Durham, 27708-0251, NC, England

    Peter Müller  & Brani Vidakovic  & 

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© 1999 Springer Science+Business Media New York

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Leporini, D., Pesquet, JC., Krim, H. (1999). Best Basis Representations with Prior Statistical Models. In: Müller, P., Vidakovic, B. (eds) Bayesian Inference in Wavelet-Based Models. Lecture Notes in Statistics, vol 141. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-0567-8_11

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  • DOI: https://doi.org/10.1007/978-1-4612-0567-8_11

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-0-387-98885-6

  • Online ISBN: 978-1-4612-0567-8

  • eBook Packages: Springer Book Archive

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