Informatics and Applications
2023, Volume 17, Issue 4, pp 2-8
NONLINEAR REGULARIZATION OF THE INVERSION OF LINEAR HOMOGENEOUS OPERATORS USING THE BLOCK THRESHOLDING METHOD
- O. V. Shestakov
- E. P. Stepanov
Abstract
The methods of thresholding the coefficients of wavelet expansions have become a popular tool for regularization of inverse statistical problems due to their simplicity, computational efficiency, and the ability to adapt both to the type of operators and to the features of the function under study. This approach proved to be the most fruitful for inversion of linear homogeneous operators arising in some signal and image processing problems.
The paper considers the block thresholding method in which the decomposition coefficients are processed in groups that allows taking into account information about neighboring coefficients. In a data model with an additive Gaussian noise, an unbiased estimate of the mean-square risk is analyzed and it is shown that under certain conditions, this estimate is strongly consistent and asymptotically normal. These properties allow constructing asymptotic confidence intervals for the theoretical mean-square risk of the method under consideration.
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[+] About this article
Title
NONLINEAR REGULARIZATION OF THE INVERSION OF LINEAR HOMOGENEOUS OPERATORS USING THE BLOCK THRESHOLDING METHOD
Journal
Informatics and Applications
2023, Volume 17, Issue 4, pp 2-8
Cover Date
2023-12-10
DOI
10.14357/19922264230401
Print ISSN
1992-2264
Publisher
Institute of Informatics Problems, Russian Academy of Sciences
Additional Links
Key words
linear homogeneous operator; wavelets; block thresholding; unbiased risk estimate; asymptotic normality; strong consistency
Authors
O. V. Shestakov  ,  ,  and E. P. Stepanov
Author Affiliations
Department of Mathematical Statistics, Faculty of Computational Mathematics and Cybernetics, M. V Lomonosov Moscow State University, 1-52 Leninskie Gory, GSP-1, Moscow 119991, Russian Federation
Moscow Center for Fundamental and Applied Mathematics, M. V. Lomonosov Moscow State University, 1 Leninskie Gory, GSP-1, Moscow 119991, Russian Federation
Federal Research Center "Computer Science and Control" of the Russian Academy of Sciences, 44-2 Vavilov Str., Moscow 119333, Russian Federation
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