We consider the problem of optical tomographic imaging in the mesoscopic regime where the photon mean-free path is on the order of the system size. It is shown that a tomographic imaging technique can be devised which is based on the assumption of single scattering and utilizes a generalization of the Radon transform which we refer to as the broken-ray transform. The technique can be used to recover the extinction coefficient of an inhomogeneous medium from angularly resolved measurements and is illustrated with numerical simulations. The forward data for these simulations were obtained by numerically solving the radiative transport equation without any approximations. Tomographic imaging in slabs of different widths was considered and it was shown that the technique can tolerate a maximum width that corresponds to approximately six scattering events. It is also shown that the use of broken rays does not result in additional ill posedness of the inverse problem in comparison to the classical problem of inverting the Radon transform. Applications to biomedical imaging are described.