Iterative Material Decomposition Method Eliminating Photoelectric Effect for Dual-MeV Energy Computed Tomography

Photons in kilovolt (kV) X-ray dual-energy computed tomography (DECT) interact with matter mainly by photoelectric effect and Compton scatter. Any material's mass attenuation coefficient (MAC) function is composed of these two effects. Thus, from a function space perspective, any MAC function can be written as a linear combination of the MAC functions of two basis materials. The projection-domain method based on this decomposition model is fit for two data sets of kV DECT. However, photons in megavolt (MV) X-ray DECT interact with matter through another way, pair production. Accordingly, three basis functions are needed to delineate this 3-D function space. Direct implementation of the projection-domain method with the decomposition model of two basis materials is feasible in spite of the unsatisfactory results. However, the projection-domain method based on the decomposition model of three basis materials becomes unsolvable, because the number of unknowns exceeds the number of data sets. Several methods add mass or volume conservation constraint to make the problem solvable, but they are not appropriate for MV DECT. We propose a new method in which the influence of photoelectric effect is numerically eliminated to regain the consistency among the decomposition model, physics model, and data sets of MV DECT. An iteration framework based on the projection-domain method with the decomposition model of two basis materials is designed to achieve this goal. The results from the numerical experiments show that the proposed method provides better decomposition coefficients and material information. Although our method is theoretically designed for element objects, water as a common compound can also be accurately decomposed. Moreover, beside the projection-domain method, the proposed one here can also be applied with other processing methods.