Identification of the coefficients in the linear Boltzmann equation by a finite number of boundary measurements

In this paper we consider an inverse problem for the time dependent linear Boltzmann equation. It concerns the identification of the coefficients via a finite number of measurements on the boundary. We prove that the total extinction coefficient and the collision kernel can be uniquely determined by at most k measurements on the boundary, provided that these coefficients belong to a finite k-dimensional vector space.