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The authors propose a dual-energy approach to reduce cone-beam artefacts in a circular orbit cone-beam computed tomography (CT) system. When there exist multiple dense structures within a large cone angle, two-pass algorithm is ineffective for reducing cone-beam artefacts because high-density materials are incorrectly segmented with simple thresholding. The proposed algorithm utilises projection data obtained with dual-energy X-ray spectra to estimate projections of the high-density materials from multi-density anatomical structures. Using bone and water as two of basis functions, the projection data of bone materials can be precisely estimated via dual-energy scans. Then, bone-only images are reconstructed by a constrained total-variation minimisation-based iterative algorithm. The reconstructed bone images are used to generate cone-beam artefacts and the final corrected images are acquired by subtracting the generated cone-beam artefacts from the original Feldkamp, Davis, and Kress images. The proposed method was validated using an extended cardiac-torso phantom with complex vertebral anatomy and compared with the two-pass algorithm. The results show that the proposed method restores distorted bony structures and intensity values, especially in regions with large cone angles. A qualitative evaluation of the mean-squared errors and structural similarities demonstrates the effectiveness of the proposed method compared to the two-pass algorithm. [ABSTRACT FROM AUTHOR]