Dual-energy CT material decomposition in the presence of nonuniqueness

<i>Objective</i>. To develop a pathlength recovery method for material decomposition to address the challenge of nonunique mappings from fluence transmission to basis material pathlengths in dual-energy computed tomography (DECT) and implement it into a two-step algorithm to reconstruct material basis maps and virtual monochromatic images (VMIs).<i>Approach.</i>By formulating the DECT imaging model as a system of implicit equations to form level curves, we present a projection-based decomposition method that explicitly accounts for cases of fluence transmissions mapping to multiple material pathlength combinations. Using numerical simulations, we investigate the method's capability to recover and analyze multiple pathlength solutions, resulting in improved material basis map reconstruction and VMI synthesis.<i>Main Results.</i>Examples of nonunique fluence mappings are demonstrated using polychromatic spectra (70 and 120 kV), demonstrating the potential for degraded material basis maps and VMI accuracy. We apply the pathlength recovery method to simulated DECT measurements of a digital phantom and demonstrate artifacts introduced by nonunique mappings if not properly resolved. A simulation with the VICTRE breast phantom is conducted to evaluate the quantitative accuracy of the method.<i>Significance.</i>This work develops a method for resolving nonunique fluence transmission to material pathlength mappings in DECT material decomposition while furthering the theoretical understanding of DECT system behaviors. Our method address efforts to enhance reliability and accuracy of material decomposition that has implications relevant to general spectral CT imaging.