Multi-Material Decomposition Methods of Dual-Energy CT Images, Revisited

In this work, we propose two algorithms suitable for multi-material decomposition (MMD) of dual-energy CT images, which exhibits a two-stage property. The first two-stage algorithm proposed in this work is equivalent to the existing method in [1]. The novelty of our proposal is that in the first stage we employ a simple left-on test algorithm to classify a voxel of the dual-CT image into two types, namely, unsolvable and solvable voxels, from a geometric point of view. In the second stage we decompose those unsolvable and solvable voxels into basis materials by the projection method and the material list method in [1], respectively. Compared to the existing method in [1], which assumes that there are at most three basis material components in each voxel and various basis material components among voxels, our second two-stage MMD algorithm relaxes such an assumption, i.e., our second two-stage MMD algorithm allows that any number (more than three) of basis material components can exist in each voxel to be considered. We achieve this by reformulating the MMD problem as a constrained minimization scheme. A patient dataset was employed to validate our proposed algorithm.