Informatics and Applications
2018, Volume 12, Issue 2, pp 11-16
UNBIASED RISK ESTIMATE OF STABILIZED HARD THRESHOLDING IN THE MODEL WITH A LONG-RANGE DEPENDENCE
Abstract
De-noising methods for processing signals and images, based on the thresholding of wavelet decomposition coefficients, have become popular due to their simplicity, speed, and the ability to adapt to signal functions that have a different degree of regularity at different locations. An analysis of inaccuracies of these methods is an important practical task, since it makes it possible to evaluate the quality of both the methods themselves and the equipment used for processing. The present author considers the recently proposed stabilized hard thresholding method which avoids the main disadvantages of the popular soft and hard thresholding techniques. The statistical properties of this method are studied. In the model with an additive Gaussian noise, the author analyzes the unbiased risk estimate. Assuming that the noise coefficients have a long-range dependence, the author formulates the conditions under which strong consistency and asymptotic normality of the unbiased risk estimate take place. The results obtained make it possible to construct asymptotic confidence intervals for the threshold processing errors using only observable data.
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[+] About this article
Title
UNBIASED RISK ESTIMATE OF STABILIZED HARD THRESHOLDING IN THE MODEL WITH A LONG-RANGE DEPENDENCE
Journal
Informatics and Applications
2018, Volume 12, Issue 2, pp 11-16
Cover Date
2018-05-30
DOI
10.14357/19922264180202
Print ISSN
1992-2264
Publisher
Institute of Informatics Problems, Russian Academy of Sciences
Additional Links
Key words
wavelets; thresholding; unbiased risk estimate; correlated noise; asymptotic normality
Authors
O.V. Shestakov  , 
Author Affiliations
Department of Mathematical Statistics, Faculty of Computational Mathematics and Cybernetics, M.V. Lomonosov Moscow State University, 1-52 Leninskiye 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
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