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- Title
Recovering a function from spherical means in 3D using local data.
- Authors
Aramyan, Rafik
- Abstract
In this article, we study the spherical mean Radon transform in $ \mathbf R^3 $ with detectors centered on a plane. A novel iterative formula to inverse the spherical mean Radon transform in $ 3D $ is presented. To recover a function from its spherical mean values we use local data which is the benefit of this formula. The inversion of the spherical mean Radon transform is used in mathematical models of radar imaging, thermo- and photo-acoustic tomography, and others.
- Subjects
SPHERICAL functions; RADON transforms; MATHEMATICAL models; INTEGRAL equations; INVERSE problems
- Publication
Inverse Problems & Imaging, 2024, Vol 18, Issue 3, p1
- ISSN
1930-8337
- Publication type
Article
- DOI
10.3934/ipi.2023050