Inverse problem for a nonlocal diffuse optical tomography equation

Abstract

In this article a nonlocal analogue of an inverse problem in diffuse optical tomography is considered. We show that whenever one has given two pairs of diffusion and absorption coefficients , , such that there holds in the measurement set W and they generate the same DN data, then they are necessarily equal in and Ω, respectively. Additionally, we show that the condition is optimal in the sense that without this restriction one can construct two distinct pairs , generating the same DN data.