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Beam hardening in x-ray computed tomography (CT) is inevitable because of the polychromatic x-ray spectrum and energy-dependent attenuation coefficients of materials, leading to the underestimation of artifacts arising from projection data, especially on metal regions. State-of-the-art research on beam-hardening artifacts is based on a numerical method that recursively performs CT reconstruction, which leads to a heavy computational burden. To address this computational issue, we propose a constrained beam-hardening estimator that provides an efficient numerical solution via a linear combination of two images reconstructed only once during the entire process. The proposed estimator reflects the geometry of metal objects and physical characteristics of beam hardening during the transmission of polychromatic x-rays through a material. Most of the associated parameters are numerically obtained from an …