Boundary reconstruction for the broken ray transform

Abstract

We reduce boundary determination of an unknown function and its normal derivatives from the (possibly weighted and attenuated) broken ray data to the injectivity of certain geodesic ray transforms on the boundary. For determination of the values of the function itself we obtain the usual geodesic ray transform, but for derivatives this transform has to be weighted by powers of the second fundamental form. The problem studied here is related to Calderón's problem with partial data.

23 pages, 1 figure; final version

Cited by in corpus (3)

• Abel transforms with low regularity with applications to X-ray tomography on spherically symmetric manifolds
• Broken ray transform for twisted geodesics on surfaces with a reflecting obstacle
• Functions of constant geodesic X-ray transform