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The Cormack inversion formula for Doppler tomography in two dimensions Научная публикация

Журнал Inverse Problems and Imaging
ISSN: 1930-8337 , E-ISSN: 1930-8345
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 Sharafutdinov Vladimir A. 1 , Vaitsel Nikita A. 1
Организации
1 Sjbolev Institute of Mathematics

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
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
Цитирование в БД: Пока нет цитирований
Альметрики: