In recent years dual-energy CT (DECT) has played a more and more important role both in medical and industrial applications because of its high detection precision and robust material identification ability. In order to reduce the hardware cost and almost no loss of reconstruction accuracy, we proposed a new DECT system with an asymmetric sandwich detector whose low-energy detector layer is normally placed while the amount of the units of the high-energy detector is much reduced. According to this DECT geometry, this paper introduced a novel DECT reconstruction method which includes four steps. Firstly, a new algorithm was proposed to recover the under-sampled high-energy projection data based on dictionary learning (DL) and total variation (TV) constraint on the CT images, which was also the main contribution of this paper. The complete low-energy data was used to reconstruct a low-energy CT image by the ART algorithm. Then, this image was used to adaptively learn the dictionary (sparsifying transform), and reconstruct the high-energy image and projection data simultaneously from highly under-sampled high-energy data. Secondly, the complete low-energy data and recovered high-energy data were used to get the integral value of Compton and photoelectric coefficients by looking up the H-L curve of different materials which was obtained by experiments. Thirdly, Compton and photoelectric coefficients were reconstructed by the ART algorithm from these integrals. Finally, the atomic number and electron density can be easily calculated from these two coefficients. Numerical simulations validated the efficiency of our algorithm to this kind of complete low-energy data and highly under-sampled high-energy data.
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