Multistatic anisotropic travel-time as a tensor tomography problem
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arXiv
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| Format: | Preprint |
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2026
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| author | Desai, Naeem Graham, Oliver Holman, Sean Lionheart, William R. B. |
| author_facet | Desai, Naeem Graham, Oliver Holman, Sean Lionheart, William R. B. |
| contents | Travel-time imaging problems seek to reconstruct an image of reflectivity of a scene by measuring travel time (and amplitude, phase) of electromagnetic or acoustic signals, such as radar and sonar. Multistatic, in this context, means that the transmitters and receivers need not be co-located. The reflectivity is anisotropic if it depends on direction, and in the multistatic case this means incoming and outgoing direction. Travel-time problems can be formulated as generalized Radon transforms of integrals over isochrones, in the planar case ellipses with transmitter and receivers at foci. In a simplified case where transmitters and receivers are distant from the scene, isochrones can be approximated by straight lines. We relate this to tensor ray transforms, specifically the longitudinal ray transform of Sharafutdinov, and discuss the implication of its known null-space. In the volumetric case isochrones are spheroids and we relate the problem to the normal Radon transform of tensor fields. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_21640 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Multistatic anisotropic travel-time as a tensor tomography problem Desai, Naeem Graham, Oliver Holman, Sean Lionheart, William R. B. Analysis of PDEs Travel-time imaging problems seek to reconstruct an image of reflectivity of a scene by measuring travel time (and amplitude, phase) of electromagnetic or acoustic signals, such as radar and sonar. Multistatic, in this context, means that the transmitters and receivers need not be co-located. The reflectivity is anisotropic if it depends on direction, and in the multistatic case this means incoming and outgoing direction. Travel-time problems can be formulated as generalized Radon transforms of integrals over isochrones, in the planar case ellipses with transmitter and receivers at foci. In a simplified case where transmitters and receivers are distant from the scene, isochrones can be approximated by straight lines. We relate this to tensor ray transforms, specifically the longitudinal ray transform of Sharafutdinov, and discuss the implication of its known null-space. In the volumetric case isochrones are spheroids and we relate the problem to the normal Radon transform of tensor fields. |
| title | Multistatic anisotropic travel-time as a tensor tomography problem |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2601.21640 |