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Emission tomography of radially symmetric objects and exponential Abelian transform

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Abstract

The properties of the exponential Abelian transform (EAT), which is defined as the exponential Radon transform (ERT) of a radially symmetric object just as the Abelian transform is the Radon transform of a radially symmetric object, are considered. A new approach to deriving the inverse EAT directly from the inverse ERT is suggested. The problems of numerical implementation of the EAT are discussed, including the problem of loss of information from deep-seated regions of the object, which is nonexistent in the case of the conventional Abel transform. The results obtained may be useful for reconstructing the spatial distribution of axisymmetric or spherically symmetric radiation sources.

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Authors and Affiliations

  1. Moscow State Institute of Electronic Technology (Technical University), Proezd 4806, 5, Zelenograd, Moscow, 124498, Russia

    S. A. Tereshchenko

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  1. S. A. Tereshchenko
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__________

Translated from Zhurnal Tekhnichesko\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{l} \) Fiziki, Vol. 75, No. 2, 2005, pp. 13–18.

Original Russian Text Copyright © 2005 by Tereshchenko.

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Tereshchenko, S.A. Emission tomography of radially symmetric objects and exponential Abelian transform. Tech. Phys. 50, 152–157 (2005). https://doi.org/10.1134/1.1866428

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  • DOI: https://doi.org/10.1134/1.1866428

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