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Λ-neighborhood wavelet shrinkage

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  • Reményi, Norbert
  • Vidakovic, Brani
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    Abstract

    We propose a wavelet-based denoising methodology based on total energy of a neighboring pair of coefficients plus their “parental” coefficient. The model is based on a Bayesian hierarchical model using a contaminated exponential prior on the total mean energy in a neighborhood of wavelet coefficients. The hyperparameters in the model are estimated by the empirical Bayes method, and the posterior mean, median and Bayes factor are obtained and used in the estimation of the total mean energy. Shrinkage of the neighboring coefficients are based on the ratio of the estimated and the observed energy. It is shown that the methodology is comparable and often superior to several existing and established wavelet denoising methods that utilize neighboring information, which is demonstrated by extensive simulations on a standard battery of test functions. An application to real-word data set from inductance plethysmography is also considered.

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    Bibliographic Info

    Article provided by Elsevier in its journal Computational Statistics & Data Analysis.

    Volume (Year): 57 (2013)
    Issue (Month): 1 ()
    Pages: 404-416

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    Handle: RePEc:eee:csdana:v:57:y:2013:i:1:p:404-416

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    Web page: http://www.elsevier.com/locate/csda

    Related research

    Keywords: Bayesian estimation; Block thresholding; Empirical Bayes method; Noncentral chi-square; Nonparametric regression;

    References

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    1. Stuart Barber & Guy P. Nason, 2004. "Real nonparametric regression using complex wavelets," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(4), pages 927-939.
    2. Abramovich, Felix & Besbeas, Panagiotis & Sapatinas, Theofanis, 2002. "Empirical Bayes approach to block wavelet function estimation," Computational Statistics & Data Analysis, Elsevier, vol. 39(4), pages 435-451, June.
    3. Anestis Antoniadis & Jeremie Bigot & Theofanis Sapatinas, . "Wavelet Estimators in Nonparametric Regression: A Comparative Simulation Study," Journal of Statistical Software, American Statistical Association, vol. 6(i06).
    4. Piotr Fryzlewicz, 2007. "Bivariate hard thresholding in wavelet function estimation," LSE Research Online Documents on Economics 25219, London School of Economics and Political Science, LSE Library.
    5. Merlise Clyde & Edward I. George, 2000. "Flexible empirical Bayes estimation for wavelets," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(4), pages 681-698.
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