Geodesic
Estimation of the average error probability when calculating wavelet coefficients in the models with a long-term dependence
Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika, no. 1 (2020), pp. 20-28

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The de-noising methods based on the threshold processing of wavelet decomposition coefficients have become popular due to their simplicity, speed, and the ability to adapt to signal functions with a varying regularity. The analysis of the errors of these methods is an important practical task, since it makes it possible to evaluate the quality of both the methods themselves and the equipment used for processing. We consider the problem of estimating the signal function from observations containing correlated noise, and evaluate the asymptotic orders of the threshold and loss functions while minimizing the average probability of the error in calculating the wavelet coefficients.
Keywords: wavelets, threshold processing, correlated noise, loss function. 
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     author = {A. A. Kudriavtsev and O. V. Shestakov},
     title = {Estimation of the average error probability when calculating wavelet coefficients in the models with a long-term dependence},
     journal = {Vestnik Tverskogo gosudarstvennogo universiteta. Seri\^a Prikladna\^a matematika},
     pages = {20--28},
     publisher = {mathdoc},
     number = {1},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VTPMK_2020_1_a1/}
}
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A. A. Kudriavtsev; O. V. Shestakov. Estimation of the average error probability when calculating wavelet coefficients in the models with a long-term dependence. Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika, no. 1 (2020), pp. 20-28. http://geodesic.mathdoc.fr/item/VTPMK_2020_1_a1/