INVERSE RADIATIVE TRANSPORT WITH LOCAL DATA

We consider a version of the inverse problem for a simple radiative transport equation (RTE) with local data, where boundary sources and mea-surements are restricted to a single subset E of the boundary of the domain S2. We show that this problem can be solved globally if the restriction of the X-ray transform to lines through E is invertible on S2. In particular, if S2 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 anal-ysis of the second term in the collision expansion for solutions to the RTE, essentially considering light which scatters exactly once inside the domain.