Inner product regularized multi-energy X-ray tomography for material decomposition

Abstract

Multi-energy X-ray tomography is studied for decomposing three materials using three X-ray energies and a classical energy-integrating detector. A regularization term is used, which includes the inner products between the material distribution functions, penalizing any overlap of different materials. An interior point method is used to solve the underlying quadratic optimization problem; a previously developed preconditioner is extended to the case with three materials, while its theoretical properties are analyzed for any number of materials. The strategy is tested on real data of a phantom embedded with Na 2 SeO 3 , Na 2 SeO 4 , and elemental selenium. These selenium-based materials exhibit K-edges suitable for investigating the proposed method. It is found that the two-dimensional distributions of selenium in different oxidation states can be mapped and distinguished from each other with the proposed algorithm. The results have applications in material science, chemistry, biology and medicine.