Informatics and Applications
December 2013, Volume 7, Issue 4, pp 75-81
INVERSION OF SPHERICAL RADON TRANSFORM IN THE CLASS OF DISCRETE RANDOM FUNCTIONS
- O. V. Shestakov
- M.G. Kuznetsova
- I.A. Sadovoy
Abstract
The paper deals with the problem of reconstructing the probabilistic distributions of random functions
from distribution of spherical projections that describe the images in certain types of tomographic experiments,
including optoacoustic tomography, thermoacoustic tomography, and radiolocation. The problems of this kind
arise when the object under study may randomly change its structure during the registration of the projection data
and the time within which its structure changes radically is considerably smaller than the time of registration of a
required number of projections. In such cases, the conventional tomographic approach cannot be used directly.
The authors assume that a randomobject may have at most countable set of structural states which are described by
integrable functions with compact support. For such discrete class of randomfunctions, the uniqueness of solution
is proved and the reconstruction method is developed which is based on the properties of the so-called moments of
projections. It is shown that the developed method is stable and gives adequate results when the projection data are
corrupted by noise.
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[+] About this article
Title
INVERSION OF SPHERICAL RADON TRANSFORM IN THE CLASS OF DISCRETE RANDOM FUNCTIONS
Journal
Informatics and Applications
December 2013, Volume 7, Issue 4, pp 75-81
Cover Date
2013-12-31
DOI
10.14357/19922264130408
Print ISSN
1992-2264
Publisher
Institute of Informatics Problems, Russian Academy of Sciences
Additional Links
Key words
randomfunctions; spherical Radon transform; stochastic tomography
Authors
O. V. Shestakov  ,M. G. Kuznetsova  , and I.A. Sadovoy
Author Affiliations
Department of Mathematical Statistics, Faculty of Computational Mathematics and Cybernetics,
M. V. Lomonosov Moscow State University; Institute of Informatics Problems, Russian Academy of Sciences, Moscow, Russia
Department of Mathematical Statistics, Faculty of Computational Mathematics and Cybernetics, M. V. Lomonosov Moscow State University, Moscow, Russia
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