An inverse problem for generalized Radon transformation

St. Petersburg Polytechnical University Journal: Physics and Mathematics

Anikonov Dmitry¹  Konovalova Dina¹  Balakina Ekaterina¹ 

[1]Sobolev Institute of Mathematics

关键词: generalized radon transformation;    integral geometry;    differential equations;    discontinuous functions;   

DOI  :  10.18721/JPM.15104

来源: DOAJ

【 摘 要 】

The paper studies the problem of inverting the integral transformation of Radon, whose formula, under traditional restrictions, gives the integrand values at any point. For the case when such a function is discontinuous and depends not only on the points of 3D space, but also on the parameters characterizing the plane of integration, these integrals have been named the generalized Radon transform (GRT). For the GRT inversion problem, the matching between quantities of known variables and variables of the integrand did not allow us to fully find the desired function. In this paper, only a part of such a function was selected, namely, the discontinuity surface of the integrand for the GRT. An algorithm for solving the problem was put forward, and it was supported by a concrete example.

【 授权许可】

Unknown