Abstract: In the reconstruction algorithm， different lookup table problems need to be set up for different objects. An algorithm based on maximum likelihood-separable paraboloidal surrogate function was proposed. A log-likelihood function， as the objective function， was constructed based on the physical model and statistical model of dual-energy CT. Separable paraboloidal surrogate function was constructed according to the convex characteristic of the objective function. The experiment result shows that， for all of the energy levels， the correlation coefficient between the image reconstructed by this method and the original image is greater than 0.983， and the signal to noise ratio is greater than 12dB， both are greater than the corresponding values of the result using the look up table algorithm. The quality of image reconstructed by the proposed method was better than the look up table method.

Key words: dual-energy CT, maximum likelihood, convex optimization, surrogate function, reconstruction algorithm