论文标题
与本地数据的逆辐射传输
Inverse Radiative Transport with Local Data
论文作者
论文摘要
我们考虑一个辐射传输方程（RTE）的逆问题，其中边界源和测量仅限于域$ω$边界的单个子集$ e $。我们表明，如果通过$ e $将X射线转换为线路对线的限制在$ω$上是可逆的，则可以在全球范围内解决此问题。特别是，如果$ω$严格凸出，我们表明，只要$ e $是边界的一个开放子集，就可以在全球范围内解决此本地数据问题。证明依赖于对RTE的碰撞扩展中第二项的隔离和分析，从本质上考虑了恰好在域内散布一次的光。
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 $Ω$. 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.
