Informatics and Applications
2025, Volume 19, Issue 1, pp 74-81
SOLVING INVERSE STATISTICAL PROBLEMS USING THRESHOLD PROCESSING METHODS THAT ALLOW THE CONSTRUCTION OF AN UNBIASED ESTIMATE OF THE MEAN-SQUARE RISK
Abstract
The methods of wavelet analysis in combination with threshold processing procedures are widely used in the tasks of estimating the signal function from noisy data. Their popularity is explained by their adaptability to the local features of the studied functions and the high speed of processing algorithms. This approach has also proved fruitful for the inversion of linear homogeneous operators that arise in some signal and image processing tasks. The most common types of threshold processing are hard and soft threshold processing. However, when using hard threshold processing, estimates with large variance are obtained and soft threshold processing leads to an additional bias. In an attempt to get rid of these disadvantages, various alternative types of threshold processing have been proposed in recent years. In this paper, the author considers a class of threshold functions that allow the construction of an unbiased estimate of the mean-square risk. This estimate makes it possible to analyze the error of noise reduction methods. The study of the properties of unbiased risk estimate is an important practical task, since it allows one to assess the quality of both the methods themselves and the equipment used. The paper discusses strategies for choosing threshold values and provides statements about the asymptotic normality and strong consistency of the risk estimate.
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[+] About this article
Title
SOLVING INVERSE STATISTICAL PROBLEMS USING THRESHOLD PROCESSING METHODS THAT ALLOW THE CONSTRUCTION OF AN UNBIASED ESTIMATE OF THE MEAN-SQUARE RISK
Journal
Informatics and Applications
2025, Volume 19, Issue 1, pp 74-81
Cover Date
2025-04-01
DOI
10.14357/19922264250110
Print ISSN
1992-2264
Publisher
Institute of Informatics Problems, Russian Academy of Sciences
Additional Links
Key words
wavelets; threshold processing; linear homogeneous operator; unbiased risk estimate
Authors
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
Federal Research Center "Computer Science and Control" of the Russian Academy of Sciences, 44-2 Vavilov Str., Moscow 119333, Russian Federation
Moscow Center for Fundamental and Applied Mathematics, M.V. Lomonosov Moscow State University, 1-52 Leninskie Gory, GSP-1, Moscow 119991, Russian Federation
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