Equivalence of computed tomography problem with the problem of recovery of functions by finite convolutions in a scheme of computational (numerical) diameter-Reference-Cited by-同舟云学术

Equivalence of computed tomography problem with the problem of recovery of functions by finite convolutions in a scheme of computational (numerical) diameter

Published:2023-12-24 Issue:12 Volume:1 Page:95-102
ISSN:2076-4626
Container-title:Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika
language:
Short-container-title:jour

Author:

Temirgaliyev N.¹,Abikenova Sh. K.¹,Azhgaliev Sh. U.¹,Nurmoldin Y. Y.¹,Taugynbayeva G. E.¹,Zhubanysheva A. Zh.¹

Affiliation:

1. L.N. Gumilyov Eurasian National University

Abstract

The equivalence of the norms of deviations of the desired density of a body from operators such as finite density transformation with specially constructed elements and the Radon transformation from it is stated. It is shown how Computer Science, previously established in the theory of Computational (Numerical) diameter, immediately leads to non-trivial results in Computed Tomography.

Publisher

Kazan Federal University

Subject

General Earth and Planetary Sciences,General Environmental Science

Reference23 articles.

1. Temirgaliev N., Taugynbaeva G.E., Zhubanysheva A.Zh. Shirokomasshtabnaya ekvivalentnost' norm preobrazovaniya Radona i porodivshei ee funktsii, Izv. vuzov. Matem. (8), 87–92 (2023).

2. Temirgaliev N., Abikenova Sh.K., Azhgaliev Sh.U., Taugynbaeva G.E., Zhubanysheva A.Zh. Teoriya preobrazovaniya Radona v kontseptsii Komp'yuternogo (vychislitel'nogo) poperechnika i metodov teorii kvazi-Monte Karlo, Vestn. Evraziisk. nats. un-ta im. L.N. Gumileva. Ser. Matem. Informatika. Mekhan. 129 (4), 89–135 (2019).

3. Temirgaliev N., Abikenova Sh.K., Azhgaliev Sh.U., Taugynbaeva G.E. Preobrazovanie Radona v skheme K(V)P-issledovanii i teorii kvazi Monte-Karlo, Izv. vuzov. Matem. (3), 98–104 (2020).

4. Natterer F. The Mathematics of Computerized Tomography (SIAM: Society for Industrial and Appl. Math., 2001).

5. Temirgaliev N., Zhubanysheva A.Zh. Poryadkovye otsenki norm proizvodnykh funktsii s nulevymi znacheniyami na lineinykh funktsionalakh i ikh primeneniya, Izv. vuzov. Matem. (3), 89–95 (2017).