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XCT with polychromatic tube spectrum causes artifact called beam hardening effect. The current correction in CT device is carried by apriori polynomial from water phantom experiment. This paper proposes a new beam hardening correction algorithm that the correction polynomial depends on the relativity of projection data in angles, which obeys Helgasson-Ludwig Consistency (HL Consistency). Firstly, a bi-polynomial is constructed to characterize the beam hardening effect based on the physical model of medical x-ray imaging. In this bi-polynomial, a factor r(γ,β) represents the ratio of the attenuation contributions caused by high density mass (bone, etc.) to low density mass (muscle, vessel, blood, soft tissue, fat, etc.) respectively in the projection angle β and fan angle γ. Secondly, let r(γ,β)=0, the bi-polynomial is degraded as a sole-polynomial. The coefficient of this polynomial can be calculated based on HL Consistency. Then, the primary correction is reached, which is also more efficient in theoretical than the correction method in current CT devices. Thirdly, based on the result of a normal CT reconstruction from the corrected projection data, r(γ,β) can be estimated. Fourthly, the coefficient of bi-polynomial can also be calculated based HL Consistency and the final correction are achieved. Experiments of circular cone beam CT indicate this method an excellent property. Correcting beam hardening effect based on HL Consistency, not only achieving a self-adaptive and more precise correction, but also getting rid of regular inconvenient water phantom experiments, will renovate the correction technique of current CT devices.
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