Summary: The mathematical formulation and numerical aspects of the inverse problem of a three-dimensional (3D) x-ray imaging method are introduced. The imaging method relies on measuring radiation scattered at two directions orthogonal to an incident beam that scans one side of the object, in addition to the traditionally recorded transmitted radiation. From this set of measurements, the inverse problem reconstructs three images: the attenuation coefficient at the incident energy, the attenuation coefficient at a scattering energy and the scattering coefficients (with the latter directly related to the electron, and hence mass density). The algorithms for this triple imaging process are presented and their numerical characteristics are discussed. With the aid of regularization and an iterative learning process, stable and bounded solutions are obtained. This 3D image-reconstruction process was able to recover the domain of interest and distinguish between different materials.