The paper considers the problem of estimating the signal function from noisy observations using threshold processing of its wavelet expansion coefficients. Under general assumptions about the properties of the noise distribution, the asymptotic order of the optimal threshold is calculated, minimizing the loss function, based on the probability that the maximum error in the wavelet coefficients exceeds a given critical level.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
D. Donoho and I. Johnstone, “Adapting to unknown smoothness via wavelet shrinkage,” J. Am. Stat. Assoc., 90, 1200–1224 (1995).
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, Berlin (2001).
J. Sadasivan, S. Mukherjee, and C. S. Seelamantula, “An optimum shrinkage estimator based on minimum-probability-of-error criterion and application to signal denoising,” in: IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), IEEE, Piscataway, NJ (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).
A. V. Markin and O. V. Shestakov, “Consistency of risk estimation with thresholding of wavelet coefficients,” Moscow Univ. Comput. Math. Cybern., 34, No. 1, 22–30 (2010).
O. V. Shestakov, “Asymptotic normality of adaptive wavelet thresholding risk estimation,” Dokl. Math., 86, No. 1, 556–558 (2012).
A. Kudryavtsev and O. Shestakov, “The asymptotic behavior of the optimal threshold minimizing the probability-of-error criterion,” J. Math. Sci., 234, No. 6, 810–815 (2018).
Author information
Authors and Affiliations
Corresponding author
Additional information
Proceedings of the XXXV International Seminar on Stability Problems for Stochastic Models, Perm, Russia, September 24–28, 2018. Part I.
Rights and permissions
About this article
Cite this article
Kudryavtsev, A.A., Shestakov, O.V. On the Choice of Thresholding Parameters for Non-Gaussian Noise Distribution. J Math Sci 246, 519–524 (2020). https://doi.org/10.1007/s10958-020-04756-7
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10958-020-04756-7