  In this paper, we consider the inverse problem of recovering a diffusion and
absorption coefficients in steady-state optical tomography problem from the
Neumann-to-Dirichlet map. We first prove a Global uniqueness and Lipschitz
stability estimate for the absorption parameter provided that the diffusion is
known. Then, we prove a Lipschitz stability result for simultaneous recovery of
diffusion and absorption. In both cases the parameters belong to a known finite
subspace with a priori known bounds. The proofs relies on a monotonicity result
combined with the techniques of localized potentials. To numerically solve the
inverse problem, we propose a Kohn-Vogeliustype cost functional over a class of
admissible parameters subject to two boundary value problems. The reformulation
of the minimization problem via the Neumann-toDirichlet operator allows us to
obtain the optimality conditions by using the Frechet differentiability of this
operator and its inverse. The reconstruction is then performed by means of an
iterative algorithm based on a quasi-Newton method. Finally, we illustrate some
numerical results.
