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Beam hardening (BH) is one of the major artifacts that severely reduces the quality of Computed Tomography (CT) imaging. In a polychromatic X-ray beam, since low-energy photons are more preferentially absorbed, the attenuation of the beam is no longer a linear function of the absorber thickness. The existing BH correction methods either require a given material, which might be unfeasible in reality, or they require a long computation time. This work aims to propose a fast and accurate BH correction method that requires no prior knowledge of the materials and corrects first and higher-order BH artifacts. In the first step, a wide sweep of the material is performed based on an experimentally measured look-up table to obtain the closest estimate of the material. Then the non-linearity effect of the BH is corrected by adding the difference between the estimated monochromatic and the polychromatic simulated projections of the segmented image. The estimated monochromatic projection is simulated by selecting the energy from the polychromatic spectrum which produces the lowest mean square error (MSE) with the acquired projection from the scanner. The polychromatic projection is estimated by minimizing the difference between the acquired projection and the weighted sum of the simulated polychromatic projections using different spectra of different filtration. To evaluate the proposed BH correction method, we have conducted extensive experiments on the real-world CT data. Compared to the state-of-the-art empirical BH correction method, the experiments show that the proposed method can highly reduce the BH artifacts without prior knowledge of the materials.