We present progress in fast, high-resolution imaging, material classification, and fault detection using
hyperspectral X-ray measurements. Classical X-ray CT approaches rely on data from many projection
angles, resulting in long acquisition and reconstruction times. Additionally, conventional CT cannot
distinguish between materials with similar densities. However, in additive manufacturing, the majority of
materials used are known a priori. This knowledge allows to vastly reduce the data collected and increase
the accuracy of fault detection. In this context, we propose an imaging method for non-destructive testing
of materials based on the combination of spectral X-ray CT and discrete tomography. We explore the
use of spectral X-ray attenuation models and measurements to recover the characteristic functions of
materials in heterogeneous media with piece-wise uniform composition. We show by means of numerical
simulation that using spectral measurements from a small number of angles, our approach can alleviate
the typical deterioration of spatial resolution and the appearance of streaking artifacts.Mechanical Engineerin