A uniqueness result for the inverse problem of identifying boundaries from weighted Radon transform
- 24 November 2022
- journal article
- research article
- Published by Walter de Gruyter GmbH in Journal of Inverse and Ill-posed Problems
- Vol. 31 (6) , 959-965
Abstract
We study the problem of the integral geometry, in which the functions are integrated over hyperplanes in the n-dimensional Euclidean space, n = 2 m + 1 {n=2m+1} . The integrand is the product of a function of n variables called the density and weight function depending on 2 n {2n} variables. Such an integration is called here the weighted Radon transform, which coincides with the classical one if the weight function is equal to one. It is proved the uniqueness for the problem of determination of the surface on which the integrand is discontinuous.Keywords
This publication has 12 references indexed in Scilit:
- The Radon Transform in the Scheme of C(N)D-Investigations and the Quasi-Monte Carlo TheoryRussian Mathematics, 2020
- Mathematical Modelling of Reconstruction of Volumetric Images in X-Ray Computed Tomography Using Holographic MethodsBulletin of the South Ural State University. Series "Mathematical Modelling, Programming and Computer Software", 2019
- Determination of Discontinuities of a Function in a Domain with Refraction from Its Attenuated Ray TransformJournal of Applied and Industrial Mathematics, 2018
- A problem of integral geometry for a family of curves with incomplete dataDoklady Mathematics, 2015
- The task of integral geometry with measure inductionComputer Research and Modeling, 2011
- Operator Theory and Ill-Posed Problems2006
- Analytic Tomography2006
- The Radon Transform1999
- Investigation of scattering and absorbing media by the methods of X-ray tomographyJournal of Inverse and Ill-posed Problems, 1993
- Plane Waves and Spherical Means1981