Informatics and Applications
2021, Volume 15, Issue 4, pp 12-19
MINIMAX ESTIMATES OF THE LOSS FUNCTION BASED ON INTEGRAL ERROR PROBABILITIES DURING THRESHOLD PROCESSING OF WAVELET COEFFICIENTS
- A. A. Kudryavtsev
- O. V. Shestakov
Abstract
Noise reduction is one of the main tasks of signal processing. Wavelet transform-based methods for solving this problem have proven to be reliable and effective. Thresholding methods that use the idea of a sparse representation of a signal function in the space of wavelet coefficients have become especially popular. These methods use fast nonlinear algorithms that adapt to the local features of the signal being processed. The parameters of these algorithms are selected based on some quality criterion or minimization of a given loss function. Most often, the mean square risk is considered as a loss function. However, in some applications, minimizing the mean square risk does not always lead to satisfactory results. In the present paper, the authors consider the loss function based on the integral probabilities of errors in calculating the wavelet coefficients. For hard and soft thresholding methods, the boundaries for the optimal threshold values are calculated and the minimax order of the considered loss function in the class of Lipschitz-regular signals is estimated.
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[+] About this article
Title
MINIMAX ESTIMATES OF THE LOSS FUNCTION BASED ON INTEGRAL ERROR PROBABILITIES DURING THRESHOLD PROCESSING OF WAVELET COEFFICIENTS
Journal
Informatics and Applications
2021, Volume 15, Issue 4, pp 12-19
Cover Date
2021-12-30
DOI
10.14357/19922264210402
Print ISSN
1992-2264
Publisher
Institute of Informatics Problems, Russian Academy of Sciences
Additional Links
Key words
wavelets; loss function; thresholding
Authors
A. A. Kudryavtsev  ,  and O. V. Shestakov , , 
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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