Regularized Material Decomposition for K-edge Separation in Hyperspectral Computed Tomography

Hyperspectral computed tomography is a developing technique that exploits the property of materials to attenuate X-rays in different quantities depending on the specific energy. It allows to not only reconstruct the object, but also to estimate the concentration of the materials which compose it. The objective of the present study is to obtain an accurate material decomposition from noisy few-projection data. A preliminary comparative study of reconstruction methods based on material decomposition is performed, employing a phantom composed of materials with similar attenuation profiles with characteristic K-edges separated by only 2, 4 and 6 keV. It is found that a one-stage method encompassing both material decomposition and tomographic reconstruction in a single variational model performs better than a more conventional two-stage approach. It is further found that better modelling of noise through use of a weighted least-squares data fidelity improves reconstruction and material separation, as does the use total variation and L1-norm regularization.