Abstract
We consider a version of the inverse problem for a simple radiative transport equation (RTE) with local data, where boundary sources and measurements are restricted to a single subset E of the boundary of the domain Ω. We show that this problem can be solved globally if the restriction of the X-ray transform to lines through E is invertible on Ω. In particular, if Ω is strictly convex, we show that this local data problem can be solved globally whenever E is an open subset of the boundary. The proof relies on isolation and analysis of the second term in the collision expansion for solutions to the RTE, essentially considering light which scatters exactly once inside the domain.
| Original language | English |
|---|---|
| Pages (from-to) | 532-541 |
| Number of pages | 10 |
| Journal | Inverse Problems and Imaging |
| Volume | 17 |
| Issue number | 2 |
| DOIs | |
| State | Published - Apr 1 2023 |
Bibliographical note
Funding Information:Acknowledgments. The author is supported in part by Simons Collaboration
Funding Information:
The author is supported in part by Simons Collaboration Grant 582020. This paper was inspired in part by the author’s attendance at the KI-Net conference on forward and inverse kinetic theory organized by Qin Li at the University of Wisconsin Madison. The author would also like to thank Plamen Stefanov for some helpful conversations.
Publisher Copyright:
© 2023, American Institute of Mathematical Sciences. All rights reserved.
Keywords
- inverse problem
- local data
- partial data
- radiative transfer
- Radiative transport
ASJC Scopus subject areas
- Analysis
- Modeling and Simulation
- Discrete Mathematics and Combinatorics
- Control and Optimization