Adaptive beam hardening correction based on projection data consistency condition

In the medical diagnostic computed tomography (CT) systems, the x-ray tube usually emits photons with a polychromatic spectrum, resulting in beam hardening artifacts in the reconstructed images. Although the bone correction method is extensively used to compensate for the beam hardening artifacts, its performance crucially depends on the empirical choice of a scaling factor. To overcome this shortcoming, here we propose two adaptive correction methods, which utilize the Helgasson-Ludwig (H-L) consistency condition to determine the optimal scaling factor and the corresponding coefficient vector. Our numerical simulation results demonstrate the effectiveness of the proposed methods.