Informatics and Applications
2021, Volume 15, Issue 3, pp 51-56
THRESHOLDING FUNCTIONS IN THE NOISE SUPPRESSION METHODS BASED ON THE WAVELET EXPANSION OF THE SIGNAL
Abstract
When transmitted over communication channels, signals are usually contaminated with noise. Noise suppression methods based on thresholding of wavelet expansion coefficients have become popular due to their simplicity, speed, and ability to adapt to nonstationary signals. The analysis of the errors of these methods is an important practical task, since it makes it possible to assess the quality of both the methods themselves and the equipment used for processing. The most popular types of thresholding are hard and soft thresholding but each has its own drawbacks. In an attempt to address these shortcomings, various alternative thresholding methods have been proposed in recent years. The paper considers a model of a signal contaminated with additive Gaussian noise and discusses the general formulation of the thresholding problem with a thresholding function belonging to a certain class. An algorithm for calculating the threshold that minimizes the unbiased risk estimate is described. Conditions are also given under which this risk estimate is asymptotically normal and strongly consistent.
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[+] About this article
Title
THRESHOLDING FUNCTIONS IN THE NOISE SUPPRESSION METHODS BASED ON THE WAVELET EXPANSION OF THE SIGNAL
Journal
Informatics and Applications
2021, Volume 15, Issue 3, pp 51-56
Cover Date
2021-09-30
DOI
10.14357/19922264210307
Print ISSN
1992-2264
Publisher
Institute of Informatics Problems, Russian Academy of Sciences
Additional Links
Key words
wavelets; thresholding; adaptive threshold; 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
Institute of Informatics Problems, 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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