Skip to Main content Skip to Navigation
Journal articles

Detection threshold for non-parametric estimation

Abstract : 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.
Complete list of metadata

Cited literature [20 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-00732333
Contributor : Abdourrahmane Mahamane Atto Connect in order to contact the contributor
Submitted on : Friday, September 14, 2012 - 5:05:28 PM
Last modification on : Monday, October 11, 2021 - 2:23:07 PM
Long-term archiving on: : Saturday, December 15, 2012 - 3:46:58 AM

File

SIVP1098Corrected.pdf
Files produced by the author(s)

Identifiers

Citation

Abdourrahmane Atto, Dominique Pastor, Grégoire Mercier. Detection threshold for non-parametric estimation. Signal, Image and Video Processing, Springer Verlag, 2008, 2 (3), pp.207-223. ⟨10.1007/s11760-008-0051-x⟩. ⟨hal-00732333⟩

Share

Metrics

Les métriques sont temporairement indisponibles