  In clinical CT, the x-ray source emits polychromatic x-rays, which are
detected in the current-integrating mode. This physical process is accurately
described by an energy-dependent non-linear integral model on the basis of the
Beer-Lambert law. However, the non-linear model is too complicated to be
directly solved for the image reconstruction, and is often approximated to a
linear integral model in the form of the Radon transform, basically ignoring
energy-dependent information. This model approximation would generate
inaccurate quantification of attenuation image and significant beam-hardening
artifacts. In this paper, we develop a deep-learning-based CT image
reconstruction method to address the mismatch of computing model to physical
model. Our method learns a nonlinear transformation from big data to correct
measured projection data to accurately match the linear integral model, realize
monochromatic imaging and overcome beam hardening effectively. The
deep-learning network is trained and tested using clinical dual-energy dataset
to demonstrate the feasibility of the proposed methodology. Results show that
the proposed method can achieve a high accuracy of the projection correction
with a relative error of less than 0.2%.
