Material classification from sparse spectral X-ray CT using vectorial total variation based on L infinity norm

The development of energy resolving photon counting detectors (PCD) has paved the way to spectral X-ray Computed Tomography (CT), with which one can simultaneously extract the energy dependence of a material's linear attenuation coefficient (LAC). Spectral CT has proved to be an advanced technique to classify materials based on their physical properties such as electron density (ρ_e) and effective atomic number (Z_eff). However, the application of spectral CT may be hindered by the poor image reconstruction quality when used for material identification in security screening where rapid scanning is required. Image reconstruction from few projections or low radiation exposure time would enable rapid scanning. The reconstruction quality for each energy bin may also be degraded since the division of photon counts into multiple energy bins naturally leads to higher noise levels. In this work, we explore how to perform accurate spectral CT reconstructions from such data, and propose L_∞norm-based vectorial total variation (L_∞-VTV) regularization that uses correlations between multiple energy bins. Using experimental data acquired with a custom laboratory instrument for spectral CT, the L_∞-VTV is tested on “real life” phantoms consisting of materials in the range of 6 ≤ Z_eff ≤ 15. For material classification from only 7 projections, the L_∞-VTV gives the relative deviations of 3.5% for ρ_e and 2.4% for Z_eff, whereas the total nuclear variation (TNV) of another state-of-the-art joint reconstruction and the total variation (TV) yield those of 3.4% and 3.1%, and 3.8% and 4.2%, respectively. The L_∞-VTV is now ready for use in security screening.