Informatics and Applications
2021, Volume 15, Issue 2, pp 30-35
ANALYSIS OF THE UNBIASED MEAN-SQUARE RISK ESTIMATE OF THE BLOCK THRESHOLDING METHOD
Abstract
Signal and image processing methods based on wavelet decomposition and thresholding have become very popular in solving problems of compression and noise suppression. This is due to their ability to adapt to local features of functions, high speed of processing algorithms and optimality of estimates obtained. In this paper, a block thresholding method is considered, in which expansion coefficients are processed in groups, which makes it possible to take into account information about neighboring coefficients. In the model with additive noise, an unbiased estimate of the mean-square risk is analyzed and it is shown that, under certain conditions of regularity, this estimate is strongly consistent and asymptotically normal. These properties allow using the risk estimate as a quality criterion for the method and constructing asymptotic confidence intervals for the theoretical mean-square risk.
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[+] About this article
Title
ANALYSIS OF THE UNBIASED MEAN-SQUARE RISK ESTIMATE OF THE BLOCK THRESHOLDING METHOD
Journal
Informatics and Applications
2021, Volume 15, Issue 2, pp 30-35
Cover Date
2021-06-30
DOI
10.14357/19922264210205
Print ISSN
1992-2264
Publisher
Institute of Informatics Problems, Russian Academy of Sciences
Additional Links
Key words
wavelets; block thresholding; mean-square risk estimate; asymptotic normality; strong consistency
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
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