Nonuniqueness in dual-energy CT

Purpose: The goal is to determine whether dual-energy computed tomography (CT) leads to a unique reconstruction using two basis materials. Methods: The beam-hardening equation is simplified to the single-voxel case. The simplified equation is rewritten to show that the solution can be considered to be linear operations in a vector space followed by a measurement model which is the sum of the exponential of the coordinates. The case of finding the concentrations of two materials from measurements of two spectra with three photon energies is the simplest non-trivial case and is considered in detail. Results: Using a material basis of water and bone, with photon energies of 30 keV, 60 keV, and 100 keV, a case with two solutions is demonstrated. Conclusions: Dual-energy reconstruction using two materials is not unique as shown by an example. Algorithms for dual-energy, dual-material reconstructions need to be aware of this potential ambiguity in the solution. Published 2017. This article is a U.S. Government work and is in the public domain in the USA.