A uniqueness result for the inverse problem of identifying boundaries from weighted Radon transform Full article
| Journal |
Journal of Inverse and Ill-Posed Problems
ISSN: 0928-0219 , E-ISSN: 1569-3945 |
||
|---|---|---|---|
| Output data | Year: 2023, Volume: 31, Number: 6, Pages: 959-965 Pages count : 7 DOI: 10.1515/jiip-2023-0038 | ||
| Tags | Weighted Radon transform; integral geometry; probing; tomography; differential equation; discontinuous functions | ||
| Authors |
|
||
| Affiliations |
|
Funding (1)
| 1 | Sobolev Institute of Mathematics | FWNF-2022-0009 |
Abstract:
We study the problem of the integral geometry, in which the functions are integrated over hyperplanes in the n-dimensional Euclidean space, n = 2m + 1. The integrand is the product of a function of n variables called the density and weight function depending on 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.
Cite:
Anikonov D.S.
, Kazantsev S.G.
, Konovalova D.S.
A uniqueness result for the inverse problem of identifying boundaries from weighted Radon transform
Journal of Inverse and Ill-Posed Problems. 2023. V.31. N6. P.959-965. DOI: 10.1515/jiip-2023-0038 WOS Scopus РИНЦ OpenAlex
A uniqueness result for the inverse problem of identifying boundaries from weighted Radon transform
Journal of Inverse and Ill-Posed Problems. 2023. V.31. N6. P.959-965. DOI: 10.1515/jiip-2023-0038 WOS Scopus РИНЦ OpenAlex
Dates:
| Submitted: | Apr 24, 2023 |
| Accepted: | Jul 29, 2023 |
| Published print: | Oct 4, 2023 |
| Published online: | Oct 4, 2023 |
Identifiers:
| Web of science: | WOS:001079744100001 |
| Scopus: | 2-s2.0-85173788825 |
| Elibrary: | 64773773 |
| OpenAlex: | W4387305297 |