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

Uniqueness, Lipschitz stability and reconstruction for the inverse optical tomography problem