New beam hardened data correction and its application to artifact reduction in CT images

Beam hardening is an unavoidable phenomenon in polychromatic CT systems, where lower-energy photons are preferentially absorbed as x-rays pass through materials such as tissue, bone, and metal. This energy-dependent attenuation, which conflicts with the monochromatic assumption in filtered back-projection (FBP), produces artifacts that degrade CT image quality and diagnostic accuracy.

This study aims to quantitatively estimate the mean energy corresponding to the beam-hardened projection data along each x-ray path and to employ this mean energy to convert energy-dependent projections into beam-hardening-corrected data. The effectiveness of the proposed mean energy-based correction method is verified through numerical simulations.

To mathematically determine the mean energy, a polynomial equation is derived whose solution represents the mean energy. Based on the Beer-Lambert law, the CT system is formulated as an energy-integrated model incorporating the x-ray spectrum and the linear attenuation coefficient of the scanned object. By applying the mean value theorem for integrals and performing power series expansions of the energy-dependent components of the attenuation coefficient-such as Compton scattering and photoelectric absorption-a polynomial equation with respect to the mean energy is obtained. Solving this equation yields the mean energy, which is subsequently employed to generate beam-hardening-corrected projection data.

A novel correction method based on the computed mean energy is proposed to transform energy-dependent projection data into corresponding monochromatic data. Numerical simulations conducted on various models demonstrate that the proposed approach effectively corrects beam-hardened projection data and substantially reduces beam-hardening artifacts in reconstructed CT images. The method maintains accuracy even in complex scenarios involving multiple overlapping materials and metallic objects, without a significant increase in computational cost. Furthermore, the robustness of the proposed correction technique is confirmed under varying x-ray spectra, verifying its potential applicability to practical CT imaging.

Grounded in physical modeling and analytical approximation, this study presents a mathematical formulation for estimating the mean energy corresponding to beam-hardened projection data and develops a correction method that effectively mitigates beam-hardening artifacts. The results highlight the potential of the proposed mean energy-based correction as a practical and computationally efficient solution for improving CT image quality. However, as this study primarily focused on the computation of mean energy as an indicator of beam-hardening severity, further research is required to apply and validate the proposed method using experimental and clinical data for comprehensive verification of its practical applicability.