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Autre Publication Scientifique Année : 2015

Optimal wavelet shrinkage of a noisy dynamical system with non-linear noise impact

Résumé

By filtering wavelet coefficients, it is possible to construct a good estimate of a pure signal from noisy data. Especially, for a simple linear noise influence, Donoho and Johnstone (1994) have already defined an optimal filter design in the sense of a good reconstruction of the pure signal. We set here a different framework where the influence of the noise is non-linear. In particular, we propose an optimal method to filter the wavelet coefficients of a discrete dynamical system disrupted by a weak noise, in order to construct good estimates of the pure signal, including Bayes' estimate, minimax estimate, oracular estimate or thresholding estimate. We present the example of a simple chaotic dynamical system as well as an adaptation of our technique in order to show empirically the robustness of the thresholding method in presence of leptokurtic noise. Moreover, we test both the hard and the soft thresholding and also another kind of smoother thresholding which seems to have almost the same reconstruction power as the hard thresholding.
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Dates et versions

halshs-01244239 , version 1 (15-12-2015)

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  • HAL Id : halshs-01244239 , version 1

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Matthieu Garcin, Dominique Guegan. Optimal wavelet shrinkage of a noisy dynamical system with non-linear noise impact. 2015. ⟨halshs-01244239⟩
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