A practical statistical polychromatic image reconstruction for computed tomography using spectrum binning

Meng Wu; Qiao Yang; Andreas Maier; Rebecca Fahrig

doi:10.1117/12.2043370

Abstract

Polychromatic statistical reconstruction algorithms have very high computational demands due to the difficulty of the optimization problems and the large number of spectrum bins. We want to develop a more practical algorithm that has a simpler optimization problem, a faster numerical solver, and requires only a small amount of prior knowledge. In this paper, a modified optimization problem for polychromatic statistical reconstruction algorithms is proposed. The modified optimization problem utilizes the idea of determining scanned materials based on a first pass FBP reconstruction to fix the ratios between photoelectric and Compton scattering components of all image pixels. The reconstruction of a density image is easy to solve by a separable quadratic surrogate algorithm that is also applicable to the multi-material case. In addition, a spectrum binning method is introduced so that the full spectrum information is not required. The energy bins sizes and attenuations are optimized based on the true spectrum and object. With these approximations, the expected line integral values using only a few energy bins are very closed to the true polychromatic values. Thus both the problem size and computational demand caused by the large number of energy bins that are typically used to model a full spectrum are reduced. Simulation showed that three energy bins using the generalized spectrum binning method could provide an accurate approximation of the polychromatic X-ray signals. The average absolute error of the logarithmic detector signal is less than 0.003 for a 120 kVp spectrum. The proposed modified optimization problem and spectrum binning approach can effectively suppress beam hardening artifacts while providing low noise images.

Citation Download Citation

Meng Wu, Meng Wu, Qiao Yang, Qiao Yang, Andreas Maier, Andreas Maier, Rebecca Fahrig, Rebecca Fahrig, "A practical statistical polychromatic image reconstruction for computed tomography using spectrum binning", Proc. SPIE 9033, Medical Imaging 2014: Physics of Medical Imaging, 90330S (19 March 2014); doi: 10.1117/12.2043370; https://doi.org/10.1117/12.2043370

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