Estimating the spectrum in computed tomography via Kullback-Leibler divergence constrained optimization.
Estimating the spectrum in computed tomography via Kullback-Leibler divergence constrained optimization.
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DOI：
10.1002/mp.13257
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发表时间：
2019-01
期刊：
影响因子：
3.8
通讯作者：
Pan X
中科院分区：
文献类型：
--
作者：
Ha W;Sidky EY;Barber RF;Schmidt TG;Pan X
我们研究了从已知体模的传输数据中进行谱估计的问题。其目标是重建能够准确模拟X射线传输曲线并反映CT系统典型能谱的真实形状的X射线谱。将谱估计问题转化为以X射线能谱为未知量的最优化问题，利用Kullback-Leibler(KL)发散约束来融合谱的先验知识，提高了估计过程的数值稳定性。所建立的约束优化问题是凸的，利用指数梯度(EG)算法可以有效地求解。在仿真数据和实验数据上验证了该方法的有效性。还讨论了与期望最大化(EM)方法的比较。在模拟中，所提出的算法被认为产生了与地面真实情况非常匹配的X射线光谱，并表示了材料中的X射线光子的衰减过程，包括和不包括在估计过程中。在实验中，计算的透射率曲线与测量的透射率曲线吻合得很好，估计的光谱呈现出物理上逼真的形状。实验结果进一步证明了该优化方法与EM方法具有相当的性能。我们的约束最优化公式为谱估计提供了一个可解释和灵活的框架。此外，KL发散约束可以包括先验光谱，并且似乎捕捉到了X射线光谱的重要特征，从而允许在CT成像中准确和稳健地估计X射线光谱。
We study the problem of spectrum estimation from transmission data of a known phantom. The goal is to reconstruct an x-ray spectrum that can accurately model the x-ray transmission curves and reflects a realistic shape of the typical energy spectra of the CT system. Spectrum estimation is posed as an optimization problem with x-ray spectrum as unknown variables, and a Kullback-Leibler (KL) divergence constraint is employed to incorporate prior knowledge of the spectrum and enhance numerical stability of the estimation process. The formulated constrained optimization problem is convex and can be solved efficiently by use of the exponentiated-gradient (EG) algorithm. We demonstrate the effectiveness of the proposed approach on the simulated and experimental data. The comparison to the expectation-maximization (EM) method is also discussed. In simulations, the proposed algorithm is seen to yield x-ray spectra that closely match the ground truth and represent the attenuation process of x-ray photons in materials, both included and not included in the estimation process. In experiments, the calculated transmission curve is in good agreement with the measured transmission curve, and the estimated spectra exhibits physically realistic looking shapes. The results further show the comparable performance between the proposed optimization-based approach and EM. Our formulation of a constrained optimization provides an interpretable and flexible framework for spectrum estimation. Moreover, a KL-divergence constraint can include a prior spectrum and appears to capture important features of x-ray spectrum, allowing accurate and robust estimation of x-ray spectrum in CT imaging.
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影响因子：
3.2
作者：
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通讯作者：
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作者：
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