  Multi-energy X-ray tomography is studied for decomposing three materials
using three X-ray energies and a classical energy-integrating detector. A novel
regularization term comprises inner products between the material distribution
functions, penalizing any overlap of different materials. The method is tested
on real data measured of a phantom embedded with Na$_2$SeO$_3$, Na$_2$SeO$_4$,
and elemental selenium. It is found that the two-dimensional distributions of
selenium in different oxidation states can be mapped and distinguished from
each other with the new algorithm. The results have applications in material
science, chemistry, biology and medicine.
