Systems and Means of Informatics
2026, Volume 36, Issue 3, pp 86-101
RISK ESTIMATION IN THE PROBLEM OF RADON TRANSFORM INVERSION USING CONTINUOUS THRESHOLD FUNCTIONS
- A. A. Kudryavtsev
- O. V. Shestakov
Abstract
Wavelet analysis methods are widely used to solve tomographic image reconstruction problems in medicine, biology, astronomy, and other fields. Their appeal lies in the speed of the algorithms, adaptability to image features, and the ability to reconstruct local image regions from incomplete projection data.
This is particularly important for medical applications where it is undesirable to expose a patient to an unnecessary radiation dose. Error analysis of these methods is an important practical task as it allows one to evaluate the quality of both the methods themselves and the equipment used. This paper considers the problem of image function reconstruction using the Radon operator inversion.
The asymptotic properties of the risk estimate are investigated under thresholding of the coefficients of the wavelet-vaguelette decomposition of the image function. Conditions are presented under which the asymptotic normality and strong consistency of the unbiased risk estimate hold.
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[+] About this article
Title
RISK ESTIMATION IN THE PROBLEM OF RADON TRANSFORM INVERSION USING CONTINUOUS THRESHOLD FUNCTIONS
Journal
Systems and Means of Informatics
Volume 36, Issue 3, pp 86-101
Cover Date
2026-11-15
DOI
10.14357/08696527260305
Print ISSN
0869-6527
Publisher
Institute of Informatics Problems, Russian Academy of Sciences
Additional Links
Key words
Radon transform; wavelet-vaguelette decomposition; thresholding; risk estimate
Authors
A. A. Kudryavtsev  ,  and 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
Moscow Center for Fundamental and Applied Mathematics, M. V. Lomonosov Moscow State University, 1 Leninskie Gory, GSP-1, Moscow 119991, Russian Federation
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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