Information Theoretic Discrepancy based Iterative Reconstruction (IDIR) Algorithm for Dual Energy X-ray Systems

In dual energy computed tomography (DECT), two sets of projection data are acquired using a couple of independent X-ray spectra. Since the attenuation characteristic of a material without a K-edge in a typical medical X-ray spectrum range is accurately described by the linear combination of two phenomena, which are the photoelectric attenuation and the Compton scatter, the DECT is theoretically capable of separating one material from another. However, the material decomposition (MD) is still a challenging problem in DECT, since two sets of sinograms from distinct X-ray spectra are not spatially aligned in practices. To avoid this problem, the MD is often achieved by a weighted summation of two reconstructed volumes that correspond to a couple of sets of projection data, which the monochromatic approximation is generally used in the reconstruction procedure. The accuracy of the MD, therefore, can be limited due to the erroneous ignorance of the energy dependency of the acquisition model. In this paper, we propose a novel algorithm, named information theoretic discrepancy based iterative reconstruction (IDIR) algorithm, for an accurate MD in dual energy X-ray systems. The generalized information theoretic discrepancy (GID) measure is newly employed as the objective value. Using particular features of the GID, a tractable objective function for the material-selective reconstruction is derived, which accounts the exact polychromatic model of transmission tomography. Since the spectral model of measured data is explicitly considered, the accurate MD is possible even for misaligned projections. In numerical experiments, the proposed method showed superior reconstruction performance over the conventional approach.