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 Cet article a éte moissonné depuis la source Math-Net.Ru

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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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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/

[1] Mallat S., A Wavelet Tour of Signal Processing, Academic Press, New York, 1999, 857 pp. | MR | Zbl

[2] Donoho D., Johnstone I., “Adapting to unknown smoothness via wavelet shrinkage”, Journal of the American Statistical Association, 90 (1995), 1200–1224 | DOI | MR | Zbl

[3] Donoho D., Johnstone I. M., “Minimax estimation via wavelet shrinkage”, Annals of Statistics, 26:3 (1998), 879–921 | DOI | MR | Zbl

[4] Jansen M., Noise Reduction by Wavelet Thresholding, v. 161, Lecture Notes in Statistics, Springer-Verlag, New York, 2001 | DOI | MR | Zbl

[5] Sadasivan J., Mukherjee S., Seelamantula C. S., “An optimum shrinkage estimator based on minimum-probability-of-error criterion and application to signal denoising”, 2014 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP, 2014, 4249–4253 | DOI

[6] Kudryavtsev A. A., Shestakov O. V., “Asymptotic Behavior of the Threshold Minimizing the Average Probability of Error in Calculation of Wavelet Coefficients”, Doklady Mathematics, 93:3 (2016), 295–299 | DOI | DOI | MR | Zbl

[7] Kudryavtsev A. A., Shestakov O. V., “The asymptotic behavior of the optimal threshold minimizing the probability-of-error criterion”, Journal of Mathematical Sciences, 234:6 (2018), 810–815 | DOI | MR | Zbl

[8] Johnstone I. M., Silverman B. W., “Wavelet threshold estimates for data with correlated noise”, Journal of the Royal Statistical Society: Series B (Statistical Methodology), 59 (1997), 319–351 | DOI | MR | Zbl

[9] Johnstone I. M., “Wavelet shrinkage for correlated data and inverse problems adaptivity results”, Statistica Sinica, 9 (1999), 51–83 | MR | Zbl