Large-Scale Equivalence of Norms of the Radon Transform and Initial Function

N. Temirgaliyev, Galiya Erbolovna Taugynbayeva, Aksaule Zhanbyrshievna Zhubanysheva

2023

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DOI 10.3103/s1066369x23080091
Data confidence 70 medium
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Abstract

Abstract This study aims to establish equivalences (in norm) of the problems of reconstructing computed tomography and computational (numerical) diameter (C(N)D), which was done in 2019 for functions of two variables. This was based on the equivalence of respective norms in the same two-dimensional Sobolev spaces proved by Frank Natterer. In this study, we prove the equivalence (in norm) of the Radon transform and the function that generated it for the case of functions of any dimension with large-scale prospects for application.