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A John's equation-based consistency condition (JECC) and restoration of corrupted projection had ever been proposed for the circular trajectory cone beam CT (CBCT) imaging. They attempted to derive the so-called JECC, i.e., a data consistency condition (DCC) from John's equation. Unfortunately, there is an imperceptible incorrectness in their derivation, which is disproved here by following the line of their thought. The basic cause leading to the imperceptible incorrectness is that John's equation was incorrectly applied to a characteristic manifold. [ABSTRACT FROM AUTHOR]

Tube of X-ray computed tomography (CT) system emitting a polychromatic spectrum of photons leads to beam hardening artifacts such as cupping and streaks, while the metal implants in the imaged object results in metal artifacts in the reconstructed images. The simultaneous emergence of various beam-hardening artifacts degrades the diagnostic accuracy of CT images in clinics. Thus, it should be deeply investigated for suppressing such artifacts. In this study, data consistency condition is exploited to construct an objective function. Non-convex optimization algorithm is employed to solve the optimal scaling factors. Finally, an optimal bone correction is acquired to simultaneously correct for cupping, streaks and metal artifacts. Experimental result acquired by a realistic computer simulation demonstrates that the proposed method can adaptively determine the optimal scaling factors, and then correct for various beam-hardening artifacts in the reconstructed CT images. Especially, as compared to the nonlinear least squares before variable substitution, the running time of the new CT image reconstruction algorithm decreases 82.36% and residual error reduces 55.95%. As compared to the nonlinear least squares after variable substitution, the running time of the new algorithm decreases 67.54% with the same residual error. [ABSTRACT FROM AUTHOR]