Abstract
The problem of nonparametric estimation of a signal function by thresholding the coefficients of its wavelet decomposition is considered. In models with various noise distributions, asymptotically optimal thresholds and orders of the loss functions are calculated on the basis of probabilities of errors in the calculation of wavelet coefficients.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
D. Donoho and I. Johnstone, J. Am. Stat. Assoc. 90, 1200–1224 (1995).
D. Donoho and I. M. Johnstone, Ann. Stat. 26 (3), 879–921 (1998).
M. Jansen, Noise Reduction by Wavelet Thresholding (Springer, New York, 2001).
J. Sadasivan, S. Mukherjee, and C. S. Seelamantula, in Proceedings of the 39th IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Florence, Italy, 2014 (Florence, 2014), pp. 4249–4253.
S. Mallat, A Wavelet Tour of Signal Processing (Academic, New York, 1999).
A. V. Markin and O. V. Shestakov, Moscow Univ. Comput. Math. Cybernet. 34 (1), 22–30 (2010).
O. V. Shestakov, Dokl. Math. 86 (1), 556–558 (2012).
A. A. Kudryavtsev and O. V. Shestakov, Dokl. Math. 93 (3), 295–299 (2016).
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © A.A. Kudryavtsev, O.V. Shestakov, 2016, published in Doklady Akademii Nauk, 2016, Vol. 471, No. 1, pp. 11–15.
Rights and permissions
About this article
Cite this article
Kudryavtsev, A.A., Shestakov, O.V. Asymptotically optimal wavelet thresholding in models with non-Gaussian noise distributions. Dokl. Math. 94, 615–619 (2016). https://doi.org/10.1134/S1064562416060028
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1064562416060028