Inverse problem for a nonlocal diffuse optical tomography equation

Abstract

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 ( γ j , q j ) , j = 1 , 2 , such that there holds q 1 = q 2 in the measurement set W and they generate the same DN data, then they are necessarily equal in R n and Ω, respectively. Additionally, we show that the condition q 1 | W = q 2 | W is optimal in the sense that without this restriction one can construct two distinct pairs ( γ j , q j ) , j = 1 , 2 generating the same DN data.