  We consider the identification of scattering and absorption rates in the
stationary radiative transfer equation. For a stable solution of this parameter
identification problem, we consider Tikhonov regularization within Banach
spaces. A regularized solution is then defined via an optimal control problem
constrained by an integro partial differential equation. By establishing the
weak-continuity of the parameter-to-solution map, we are able to ensure the
existence of minimizers and thus the well-posedness of the regularization
method. In addition, we prove certain differentiability properties, which allow
us to construct numerical algorithms for finding the minimizers and to analyze
their convergence. Numerical results are presented to support the theoretical
findings and illustrate the necessity of the assumptions made in the analysis.
