  Dual-energy X-ray tomography is considered in a context where the target
under imaging consists of two distinct materials. The materials are assumed to
be possibly intertwined in space, but at any given location there is only one
material present. Further, two X-ray energies are chosen so that there is a
clear difference in the spectral dependence of the attenuation coefficients of
the two materials. A novel regularizer is presented for the inverse problem of
reconstructing separate tomographic images for the two materials. A combination
of two things, (a) non-negativity constraint, and (b) penalty term containing
the inner product between the two material images, promotes the presence of at
most one material in a given pixel. A preconditioned interior point method is
derived for the minimization of the regularization functional. Numerical tests
with digital phantoms suggest that the new algorithm outperforms the baseline
method, Joint Total Variation regularization, in terms of correctly
material-characterized pixels. While the method is tested only in a
two-dimensional setting with two materials and two energies, the approach
readily generalizes to three dimensions and more materials. The number of
materials just needs to match the number of energies used in imaging.
