Segmentation-free quasi-Newton method for polyenergetic CT reconstruction

X-ray polychromaticity is a well-known source of artifacts in clinical CT imaging. As a polyenergetic X-ray beam passes through an object, rays with lower energy are preferentially attenuated, and thus the spectrum of the beam becomes increasingly skewed towards high-energy rays. This beam hardening phenomenon results in inconsistent projection data, and produces artifacts in images reconstructed using filtered backprojection (FBP). Methods for reducing or eliminating beam hardening artifacts can be broadly categorized into postreconstruction approaches, which attempt to eliminate artifacts from an image reconstructed using FBP, or iterative reconstruction approaches, which attempt to reconstruct an artifact free image from the projection data, by incorporating X-ray polychromaticity directly into the system model. In this paper we compare a well-known post-reconstruction approach with an iterative approach that uses a quasi-Newton minimization algorithm. The post-reconstruction approach is a two-step process consisting of a soft-tissue correction and bone correction, while our iterative approach is based on modeling energy-dependent attenuation coefficients as a sum of photoelectric and Compton scattering components. Two numerical phantom experiments are used to demonstrate that the postreconstruction approach does not compensate for artifacts caused by more than one different type of high attenuation material, while the iterative approach is able to reconstruct artifact-free images in both experiments. The presented iterative approach does not require any segmentation and can readily incorporate attenuation models other than the one used in this paper.