Reconstruction of the coefficients of the stationary transport equation from boundary measurements

We study the inverse problem of recovering the absorption coefficient sigma(a)(x, \v\) and the collision kernel k(x, v', v) in the stationary linear Boltzmann equation in a bounded domain from the albedo operator on the boundary. We show that under some conditions on the coefficients that guarantee well-posedness of the direct problem, the inverse problem has a unique solution. Moreover, we provide explicit formulae for recovering sigma(a), k.