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Convergence and performance of the peeling wavelet denoising algorithm

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  • Céline Lacaux
  • Aurélie Muller-Gueudin
  • Radu Ranta
  • Samy Tindel

Abstract

This note is devoted to an analysis of the so-called peeling algorithm in wavelet denoising. Assuming that the wavelet coefficients of the useful signal are modeled by generalized Gaussian random variables and its noisy part by independent Gaussian variables, we compute a critical thresholding constant for the algorithm, which depends on the shape parameter of the generalized Gaussian distribution. We also quantify the optimal number of steps which have to be performed, and analyze the convergence of the algorithm. Several implementations are tested against classical wavelet denoising procedures on benchmark and simulated biological signals. Copyright Springer-Verlag Berlin Heidelberg 2014

Suggested Citation

  • Céline Lacaux & Aurélie Muller-Gueudin & Radu Ranta & Samy Tindel, 2014. "Convergence and performance of the peeling wavelet denoising algorithm," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 77(4), pages 509-537, May.
    • Handle: RePEc:spr:metrik:v:77:y:2014:i:4:p:509-537
    DOI: 10.1007/s00184-013-0451-y
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    References listed on IDEAS

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    1. Antoniadis, Anestis & Bigot, Jeremie & Sapatinas, Theofanis, 2001. "Wavelet Estimators in Nonparametric Regression: A Comparative Simulation Study," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 6(i06).
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    Cited by:

    1. Müller K. & Richter W.-D., 2017. "Exact distributions of order statistics from ln,p-symmetric sample distributions," Dependence Modeling, De Gruyter, vol. 5(1), pages 221-245, August.

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