Inverse Radiative Transport with Local Data

DOI10.3934/IPI.2022071arXiv2001.11460MaRDI QIDQ6333815

Francis J. Chung

Publication date: 30 January 2020

Abstract: We consider an inverse problem for a radiative transport equation (RTE) in which boundary sources and measurements are restricted to a single subset $E$ of the boundary of the domain $Omega$. We show that this problem can be solved globally if the restriction of the X-ray transform to lines through $E$ is invertible on $Omega$. In particular, if $Omega$ 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.

Mathematics Subject Classification ID

Inverse problems for PDEs (35R30) Transport equations (35Q49)

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