Informatics and Applications
2016, Volume 10, Issue 2, pp 65-69
STATISTICAL PROPERTIES OF THE DENOISING METHOD BASED ON THE STABILIZED HARD THRESHOLDING
Abstract
The thresholding techniques for the wavelet coefficients of the signal and image functions have become a popular denoising tool because of their simplicity, computational efficiency, and possibility to adapt to the functions with different amounts of smoothness in different locations. The paper 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. The unbiased risk estimate is analyzed in the model with an additive Gaussian noise. Wavelet thresholding risk analysis is an important practical task, because it allows determining the quality of the techniques themselves and the equipment which is being used. The paper proves that under certain conditions, the unbiased risk estimate is strongly consistent and asymptotically normal. These properties allow constructing the asymptotic confidence intervals for the theoretical mean squared risk of the method.
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[+] About this article
Title
STATISTICAL PROPERTIES OF THE DENOISING METHOD BASED ON THE STABILIZED HARD THRESHOLDING
Journal
Informatics and Applications
2016, Volume 10, Issue 2, pp 65-69
Cover Date
2016-05-30
DOI
10.14357/19922264160207
Print ISSN
1992-2264
Publisher
Institute of Informatics Problems, Russian Academy of Sciences
Additional Links
Key words
wavelets; thresholding; unbiased 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 Leninskiye Gory, GSP-1, Moscow 119991, Russian Federation
Institute of Informatics Problems, Federal Research Center “Computer Sciences and Control” of the Russian
Academy of Sciences, 44-2 Vavilov Str.,Moscow 119333, Russian Federation
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