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Journal of Mathematical Sciences

, Volume 237, Issue 6, pp 804–809 | Cite as

Estimation of the Loss Function When Using Wavelet-Vaguelette Decomposition for Solving Ill-Posed Problems

  • A. A. KudryavtsevEmail author
  • O. V. Shestakov
Article

The paper discusses the de-noising method in a model with an additive Gaussian noise, based on the wavelet-vaguelette decomposition and thresholding of the vaguelette coefficients. For soft and hard thresholding procedures, we derive the values of the thresholds and estimate asymptotically optimal orders of the loss function based on the probabilities of errors in calculating decomposition coefficients.

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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Mathematical Statistics, Faculty of Computational Mathematics and CyberneticsM. V. Lomonosov Moscow State UniversityMoscowRussia
  2. 2.Institute of Informatics ProblemsFederal Research Center “Computer Science and Control” of the Russian Academy of SciencesMoscowRussia

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