Our work focuses on developing a fast MAR method based on a constrained beam-hardening estimator representing the underestimated error between the expected and calculated reconstruction images. The proposed estimator is derived from a polychromatic X-ray attenuation model with respect to the X-ray transmission length, avoiding dependencies regarding the X-ray spectrum and material attenuation coefficients. It maximizes the accuracy for the correction of beam-hardening artifacts by analyzing the change in the attenuation coefficient level while polychromatic X-ray passes through a homogeneous metallic material. The entire process is completed by a linear combination of two images reconstructed only once, leading to faster computation. The estimator-associated parameters are numerically calculated from an uncorrected CT image and metal-only forward projection. The only unknown parameter to minimize the beam-hardening artifact is fine-tuned by solving linear optimization on the reconstruction image domain without forward and backward projection transformations. This method is sufficiently effective in terms of the optimization speed and quality in MAR, compared with other beam-hardening correction methods.
Comparison among LIMAR, NMAR, BCMAR, and the proposed method for the JawSimulationPhantom (Cu). From left, the uncorrected image, LIMAR result, NMAR result, BCMAR result, and the result of the proposed method are shown. The first row shows the results of each method, and the second row shows the difference images for each result with respect to the ground truth.