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Inform. Primen., 2019, Volume 13, Issue 1, Pages 49–54 (Mi ia577)  

Inversion of homogeneous operators using stabilized hard thresholding with unknown noise variance

O. V. Shestakovab

a 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
b 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

Abstract: When inverting linear homogeneous operators, it is necessary to use regularization methods, since observed data are usually noisy. For noise suppression, threshold processing of wavelet coefficients of the observed signal function is often used. Threshold processing has become a popular noise suppression tool due to its simplicity, computational efficiency, and ability to adapt to functions that have different degrees of regularity at different domains. The paper discusses the recently proposed stabilized hard thresholding method that eliminates the main drawbacks of soft and hard thresholding methods and studies statistical properties of this method. In the data model with an additive Gaussian noise with unknown variance, an unbiased estimate of the mean square risk is analyzed and it is shown that under certain conditions, this estimate is asymptotically normal and the variance of the limit distribution depends on the type of estimate of noise variance.

Keywords: wavelets, threshold processing, unbiased risk estimate, asymptotic normality, strong consistency.

Funding Agency Grant Number
Russian Foundation for Basic Research 19-07-00352
This research was partly supported by the Russian Foundation for Basic Research (project No. 19-07-00352).


DOI: https://doi.org/10.14357/19922264190107

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Received: 14.12.2018

Citation: O. V. Shestakov, “Inversion of homogeneous operators using stabilized hard thresholding with unknown noise variance”, Inform. Primen., 13:1 (2019), 49–54

Citation in format AMSBIB
\Bibitem{She19}
\by O.~V.~Shestakov
\paper Inversion of~homogeneous operators using~stabilized hard thresholding with~unknown noise variance
\jour Inform. Primen.
\yr 2019
\vol 13
\issue 1
\pages 49--54
\mathnet{http://mi.mathnet.ru/ia577}
\crossref{https://doi.org/10.14357/19922264190107}
\elib{http://elibrary.ru/item.asp?id=37170982}


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