Iterative reconstruction of the electron density and effective atomic number using a non-linear forward model

Abstract

For material identification, characterization, and quantification, it is useful to estimate system-independent material properties that do not depend on the detailed specifications of the X-ray computed tomography (CT) system such as spectral response. System independent ρ_e and Z_e (SIRZ) refers to a suite of methods for estimating the system independent material properties of electron density (ρ_e) and effective atomic number (Z_e) of an object scanned using dual-energy X-ray CT (DECT). The current state-of-the-art approach, SIRZ-2, makes certain approximations that lead to inaccurate estimates for large atomic numbered (Z_e) materials. In this paper, we present an extension, SIRZ-3, which iteratively reconstructs the unknown ρ_e and Z_e while avoiding the limiting approximations made by SIRZ-2. Unlike SIRZ-2, this allows SIRZ-3 to accurately reconstruct ρe and Z_e even at large Z_e. SIRZ-3 relies on the use of a new non-linear differentiable forward measurement model that expresses the DECT measurement data as a direct analytical function of ρ_e and Z_e. Leveraging this new forward model, we use an iterative optimization algorithm to reconstruct (or solve for) ρ_e and Z_e directly from the DECT data. Compared to SIRZ-2, we show that the magnitude of performance improvement using SIRZ-3 increases with increasing values for Z_e.