The Cormack inversion formula for Doppler tomography in two dimensions Научная публикация
| Журнал |
Inverse Problems and Imaging
ISSN: 1930-8337 , E-ISSN: 1930-8345 |
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| Вых. Данные | Год: 2025, Том: 21, Номер статьи : 002, Страниц : 30 DOI: 10.3934/ipi.2026002 | ||
| Ключевые слова | Cormack inversion formula, Doppler transform, exterior problem, solenoidal part of a vector field, Mellin transform | ||
| Авторы |
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| Организации |
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Информация о финансировании (1)
| 1 | Министерство науки и высшего образования РФ | FWNF-2026-0026 |
Реферат:
The ray transform $I$ (also called the Doppler transform) measures the work of a vector field over lines. The operator $I$ has a nontrivial kernel, only the solenoidal part of a vector field $f$ can be recovered from $If$.
In the two-dimensional case, we derive an analogoue of the Cormack inversion formula which recovers a solenoidal vector field from integrals measured over lines that do not intersect a certain disk.
Then we study the exterior problem for the two-dimensional Doppler transform in two cases: (1) for vector fields defined in a bounded annulus and (2) for vector fields in an unbounded annulus. The theorem on decomposition of a vector field into solenoidal and potential parts is proved in both cases. These two theorems are very different; in particular, the decomposition is not unique in the case of an unbounded annulus. The algorithm of recovering the solenoidal part of a vector field is presented in both cases.
Finally a numerical example of reconstructing a solenoidal vector field is presented.
Библиографическая ссылка:
Sharafutdinov V.A.
, Vaitsel N.A.
The Cormack inversion formula for Doppler tomography in two dimensions
Inverse Problems and Imaging. 2025. V.21. 002 :1-30. DOI: 10.3934/ipi.2026002 WOS
The Cormack inversion formula for Doppler tomography in two dimensions
Inverse Problems and Imaging. 2025. V.21. 002 :1-30. DOI: 10.3934/ipi.2026002 WOS
Даты:
| Поступила в редакцию: | 22 мар. 2025 г. |
| Принята к публикации: | 5 авг. 2025 г. |
| Опубликована в печати: | 16 нояб. 2025 г. |
| Опубликована online: | 16 нояб. 2025 г. |
Идентификаторы БД:
| Web of science: | WOS:001625137800001 |
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