Signal, Image and Video Processing

, Volume 2, Issue 3, pp 207–223 | Cite as

Detection threshold for non-parametric estimation

  • Abdourrahmane M. AttoEmail author
  • Dominique Pastor
  • Gregoire Mercier
Original Paper


A new threshold is presented for better estimating a signal by sparse transform and soft thresholding. This threshold derives from a non-parametric statistical approach dedicated to the detection of a signal with unknown distribution and unknown probability of presence in independent and additive white Gaussian noise. This threshold is called the detection threshold and is particularly appropriate for selecting the few observations, provided by the sparse transform, whose amplitudes are sufficiently large to consider that they contain information about the signal. An upper bound for the risk of the soft thresholding estimation is computed when the detection threshold is used. For a wide class of signals, it is shown that, when the number of observations is large, this upper bound is from about twice to four times smaller than the standard upper bounds given for the universal and the minimax thresholds. Many real-world signals belong to this class, as illustrated by several experimental results.


Non-parametric estimation Soft thresholding Sparse transform Wavelet transform Non-parametric detection 


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Copyright information

© Springer-Verlag London Limited 2008

Authors and Affiliations

  • Abdourrahmane M. Atto
    • 1
    Email author
  • Dominique Pastor
    • 1
  • Gregoire Mercier
    • 1
  1. 1.Institut TelecomTelecom Bretagne, CNRS UMR 2872 TAMCIC, CS 83818Brest Cedex 3France

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