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The photon distribution, as a function of position, angle, and time, is computed using the analytical cumulant solution of the Boltzmann radiative transfer equation (RTE). A linear forward model for light propagation in turbid media for three-dimensional (3-D) optical tomography is formed based on this solution. The model can be used with time resolved, continuous wave (CW), and frequency-domain measurements in parallel geometries. This cumulant forward model (CFM) is more accurate than that based on the diffusion approximation of RTE. An inverse algorithm that incorporates this CFM is developed, based on a fast 3-D hybrid-dual-Fourier tomographic approach using multiple detectors and multiple sources in parallel geometries. The inverse algorithm can produce a 3-D image of a turbid medium with more than 20 000 voxels in 1-2 min using a personal computer. A 3-D image reconstructed from simulated data is presented.