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Recently taking advantage of the novel diffraction-enhanced imaging (DEI) method, one very effective and practical phase contrast imaging technique—a new x-ray computed tomography scheme based on DEI (DEI-CT) showed promising results, really superior to those of conventional CT imaging. In this letter, we show that the application of the conventional CT reconstruction algorithm is not always satisfactory for the new DEI-CT imaging and a new mathematical framework for imaging reconstruction is presented. Experimental data collected at the Beijing synchrotron radiation facility are also discussed using the new algorithm.