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(copyright) 2022 Institute of Physics and Engineering in Medicine.Objective. The polychromatic nature of the x-ray spectrum in computed tomography leads to two types of artifacts in the reconstructed image: cupping in homogeneous areas and dark bands between dense parts, such as bones. This fact, together with the energy dependence of the mass attenuation coefficients of the tissues, results in erroneous values in the reconstructed image. Many post-processing correction schemes previously proposed require either knowledge of the x-ray spectrum or the heuristic selection of some parameters that have been shown to be suboptimal for correcting different slices in heterogeneous studies. In this study, we propose and validate a method to correct the beam hardening artifacts that avoids such restrictions and restores the quantitative character of the image. Approach. Our approach extends the idea of the water-linearization method. It uses a simple calibration phantom to characterize the attenuation for different soft tissue and bone combinations of the x-ray source polychromatic beam. The correction is based on the bone thickness traversed, obtained from a preliminary reconstruction. We evaluate the proposed method with simulations and real data using a phantom composed of PMMA and aluminum 6082 as materials equivalent to water and bone. Main results. Evaluation with simulated data showed a correction of the artifacts and a recovery of monochromatic values similar to that of the post-processing techniques used for comparison, while it outperformed them on real data. Significance. The proposed method corrects beam hardening artifacts and restores monochromatic attenuation values with no need of spectrum knowledge or heuristic parameter tuning, based on the previous acquisition of a very simple calibration phantom.