Recovery of coefficients in the linear Boltzmann equation

In this paper, we treat the inverse problem of determining the scattering coefficient and the absorption coefficient appearing in the linear Boltzmann equation via boundary measurements. We show that the gauge-equivalent of the coefficients yields the same albedo operator. The albedo operator is defined as the mapping from the incoming boundary conditions to the outgoing transport solution at the boundary of a bounded and convex domain. We study the stability of the absorption coefficient up to a gauge transformation from the albedo operator, and we prove that the scattering time-dependent coefficient can be uniquely determined in a precise subset of domain, from the albedo operator. Published under license by AIP Publishing.