Signal denoising methods based on the threshold processing of wavelet coefficients are widely used in various application areas. When applying these methods, it is usually assumed that the number of wavelet coefficients is fixed, and the noise distribution is Gaussian. Such a model has been well studied in the literature, and optimal threshold values have been calculated for different signal classes and loss functions. However, in some situations the sample size is not known in advance and is modeled by a random variable. In this paper, we consider a model with a random number of observations contaminated by a Gaussian noise, and study the behavior of the loss function based on the probabilities of errors in calculating wavelet coefficients for a growing sample size.
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D. Donoho and I. M. Johnstone, “Ideal spatial adaptation via wavelet shrinkage,” Biometrika, 81, No. 3, 425–455 (1994).
D. Donoho and I. M. Johnstone, “Minimax estimation via wavelet shrinkage,” Ann. Stat., 26, No. 3, 879–921 (1998).
M. Jansen, Noise Reduction by Wavelet Thresholding, Springer, New York (2001).
J. Sadasiva, S. Mukherjee, and C. S. Seelamantula, “An optimum shrinkage estimator based on minimum-probability-of-error criterion and application to signal denoising,” in: 2014 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Piscataway, New Jersey (2014), pp. 4249–4253.
A. A. Kudryavtsev and O. V. Shestakov, “Asymptotic behavior of the threshold minimizing the average probability of error in calculation of wavelet coefficients,” Dokl. Math., 93, No. 3, 295–299 (2016).
A. A. Kudryavtsev and O. V. Shestakov, “Asymptotically optimal wavelet thresholding in the models with non-Gaussian noise distributions,” Dokl. Math., 94, No. 3, 615–619 (2016).
S. Mallat, A Wavelet Tour of Signal Processing, Academic Press, New York (1999).
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Proceedings of the XXXIV International Seminar on Stability Problems for Stochastic Models, Debrecen, Hungary.
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Shestakov, O.V. Averaged Probability of the Error in Calculating Wavelet Coefficients for the Random Sample Size. J Math Sci 237, 826–830 (2019). https://doi.org/10.1007/s10958-019-04209-w
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DOI: https://doi.org/10.1007/s10958-019-04209-w