Abstract. In current Xray CT scanners, tomographic reconstruction relies only on directly transmitted photons. The models used for reconstruction have regarded photons scattered by the body as noise or disturbance to be disposed of, either by acquisition hardware (an antiscatter grid) or by the reconstruction software. This increases the radiation dose delivered to the patient. Treating these scattered photons as a source of information, we solve an inverse problem based on a 3D radiative transfer model that includes both elastic (Rayleigh) and inelastic (Compton) scattering. We further present ways to make the solution numerically efficient. The resulting tomographic reconstruction is more accurate than traditional CT, while enabling significant dose reduction and chemical decomposition. Demonstrations include both simulations based on a standard medical phantom and a real scattering tomography experiment.