Identification of inhomogeneous matter by pulsed multienergy tomography methods

Nazarov V.G., Prokhorov I.V., Yarovenko I.P.
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The article considers the mathematical aspects of the problem of identifying a multicomponent scattering medium based on pulsed multienergy X-ray irradiation data. X-ray diagnostics problems are of considerable interest from both theoretical and practical points of view, and radiographic methods are indispensable in non-destructive testing of products.

Within the framework of a mathematical model based on a non-stationary integro-differential equation of radiation transfer, the inverse problem of finding the attenuation coefficient for radiation known at the boundary of the region and the problem of identifying a substance based on the found values of the attenuation coefficient on a discrete set of irradiation energies of the medium are formulated.

A preliminary processing of a wide list of substances of interest in computed tomography was carried out to determine the possibility of their identification by an approximately specified radiation attenuation coefficient characterizing the medium. When analyzing the degree of proximity of substances in a certain norm, it was found that the set of all possible substances potentially contained in the medium is divided into a finite number of non-intersecting clusters. For a sufficiently short duration of the probing signal, the scattering component of the radiation leaving the medium is asymptotically small. This circumstance allows us to reduce the inverse problem for the radiation transfer equation to the problem of inverting the Radon transform from the attenuation coefficient. The possibility of unambiguous or partial identification of a substance by varying the duration of the probing pulse and the number of energy levels of irradiation of the medium is analyzed using numerical modeling methods on a specially developed digital phantom.

Keywords: pulse tomography, non-stationary radiation transfer equation, inverse problems, attenuation coefficient, substance identification, multi-energy probing
Citation in English: Nazarov V.G., Prokhorov I.V., Yarovenko I.P. Identification of inhomogeneous matter by pulsed multienergy tomography methods // Computer Research and Modeling, 2025, vol. 17, no. 4, pp. 621-639
Citation in English: Nazarov V.G., Prokhorov I.V., Yarovenko I.P. Identification of inhomogeneous matter by pulsed multienergy tomography methods // Computer Research and Modeling, 2025, vol. 17, no. 4, pp. 621-639
DOI: 10.20537/2076-7633-2025-17-4-621-639
URL: http://crm-en.ics.org.ru/journal/article/3633/
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Copyright © 2025 Nazarov V.G., Prokhorov I.V., Yarovenko I.P.

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