Informatics and Applications
2017, Volume 11, Issue 2, pp 117-121
STRONG CONSISTENCY OF THE MEAN SQUARE RISK ESTIMATE IN THE INVERSE STATISTICAL PROBLEMS
Abstract
Nonlinear methods of digital signal processing based on thresholding of wavelet coefficients became a popular tool for solving the problems of signal de-noising and compression. This is explained by the fact that the wavelet methods allow much more effective analysis of nonstationary signals than traditional Fourier analysis, thanks to the better adaptation to the functions with varying degrees of regularity Wavelet thresholding risk analysis is an imp ortant practical task, because it allows determining the quality of techniques themselves and the equipment which is being used. In some applications, the data are observed not directly but after applying a linear transformation. The problem of inverting this transformation is usually set incorrectly, leading to an increase in the noise variance. In this paper, the asymptotic properties of the mean square error (MSE) estimate are studied when inverting linear homogeneous operators by means of wavelet vaguelette decomposition and thresholding. The strong consistency of this estimate has been proved under mild conditions.
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[+] About this article
Title
STRONG CONSISTENCY OF THE MEAN SQUARE RISK ESTIMATE IN THE INVERSE STATISTICAL PROBLEMS
Journal
Informatics and Applications
2017, Volume 11, Issue 2, pp 117-121
Cover Date
2017-06-30
DOI
10.14357/19922264170213
Print ISSN
1992-2264
Publisher
Institute of Informatics Problems, Russian Academy of Sciences
Additional Links
Key words
wavelets; thresholding; MSE 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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