Informatics and Applications
2014, Volume 8, Issue 1, pp 36-44
ASYMPTOTIC PROPERTIES OF WAVELET THRESHOLDING RISK ESTIMATE IN THE MODEL OF DATA WITH CORRELATED NOISE
- A.A. Eroshenko
- O. V. Shestakov
Abstract
Wavelet thresholding techniques of denoising are widely used in signal and image processing. These
methods are easily implemented through fast algorithms; so, they are very appealing in practical situations. Besides,
they adapt to function classes with different amounts of smoothness in different locations more effectively than the
usual linear methods. Wavelet thresholding risk analysis is an important practical task because it allows determining
the quality of techniques themselves and equipment which is being used. In the present paper, asymptotical
properties of mean-square risk estimate of wavelet thresholding techniques have been studied in the model of data
with correlated noise. The conditions under which the unbiased risk estimate is consistent and asymptotically
normal are given. These results allow constructing asymptotical confidence intervals for wavelet thresholding risk,
using only the observed data.
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[+] About this article
Title
ASYMPTOTIC PROPERTIES OF WAVELET THRESHOLDING RISK ESTIMATE IN THE MODEL OF DATA WITH CORRELATED NOISE
Journal
Informatics and Applications
2014, Volume 8, Issue 1, pp 36-44
Cover Date
2014-03-31
DOI
10.14357/19922264140105
Print ISSN
1992-2264
Publisher
Institute of Informatics Problems, Russian Academy of Sciences
Additional Links
Key words
wavelets; unbiased risk estimate; correlated noise; asymptotic normality
Authors
A.A. Eroshenko  and O. V. Shestakov , 
Author Affiliations
M.V. Lomonosov Moscow State University, Faculty of Computational Mathematics and Cibernetics,
1-52 Leninskiye Gory, GSP-1,Moscow 119991, Russian Federation
Institute of Informatics Problems, Russian Academy of Sciences, 44-2 Vavilov Str.,Moscow 119333, Russian
Federation
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