Email this article Estimation of the Loss Function When Using Wavelet-Vaguelette Decomposition for Solving Ill-Posed Problems
- Authors: Kudryavtsev A.A.1, Shestakov O.V.2
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Affiliations:
- Department of Mathematical Statistics, Faculty of Computational Mathematics and Cybernetics, M. V. Lomonosov Moscow State University
- Institute of Informatics Problems, Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences
- Issue: Vol 237, No 6 (2019)
- Pages: 804-809
- Section: Article
- URL: https://journals.rcsi.science/1072-3374/article/view/242456
- DOI: https://doi.org/10.1007/s10958-019-04206-z
- ID: 242456
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Abstract
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.
About the authors
A. A. Kudryavtsev
Department of Mathematical Statistics, Faculty of Computational Mathematics and Cybernetics, M. V. Lomonosov Moscow State University
Author for correspondence.
Email: nubigena@mail.ru
Russian Federation, Moscow
O. V. Shestakov
Institute of Informatics Problems, Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences
Email: nubigena@mail.ru
Russian Federation, Moscow
