Informatics and Applications
2022, Volume 16, Issue 4, pp 14-19
UNBIASED THRESHOLDING RISK ESTIMATE WITH TWO THRESHOLD VALUES
Abstract
The problems of noise reduction in signals arise in many application areas. In cases where the signals are not stationary, noise suppression methods based on wavelet transform and thresholding procedures have proven themselves well. These methods are computationally efficient and adapt well to the local features of the signals.
The most common types of thresholding are hard and soft thresholding. However, when using hard thresholding, estimates with large variance are obtained, and soft thresholding leads to additional bias. In an attempt to get rid of these shortcomings, various alternative types of thresholding have been proposed in recent years. This paper considers a thresholding procedure with two thresholds which behaves as soft thresholding for small values of wavelet coefficients and as hard thresholding for the large ones. For this type of thresholding, an unbiased estimate of the mean-square risk is constructed and its statistical properties are analyzed. An algorithm for calculating the threshold values that minimizes this estimate is described.
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[+] About this article
Title
UNBIASED THRESHOLDING RISK ESTIMATE WITH TWO THRESHOLD VALUES
Journal
Informatics and Applications
2022, Volume 16, Issue 4, pp 14-19
Cover Date
2022-12-30
DOI
10.14357/19922264220403
Print ISSN
1992-2264
Publisher
Institute of Informatics Problems, Russian Academy of Sciences
Additional Links
Key words
wavelets; thresholding; 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 Leninskie Gory, GSP-1, Moscow 119991, Russian Federation
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