CEA, LIST, 91191 Gif-sur-Yvette, France and CNRS, SUPELEC, UNIV PARIS SUD, L2S, 3 rue Joliot-Curie, 91192 Gif-sur-Yvette, France.
Med Phys. 2013 Nov;40(11):111916. doi: 10.1118/1.4820478.
Dual-energy computed tomography (DECT) makes it possible to get two fractions of basis materials without segmentation. One is the soft-tissue equivalent water fraction and the other is the hard-matter equivalent bone fraction. Practical DECT measurements are usually obtained with polychromatic x-ray beams. Existing reconstruction approaches based on linear forward models without counting the beam polychromaticity fail to estimate the correct decomposition fractions and result in beam-hardening artifacts (BHA). The existing BHA correction approaches either need to refer to calibration measurements or suffer from the noise amplification caused by the negative-log preprocessing and the ill-conditioned water and bone separation problem. To overcome these problems, statistical DECT reconstruction approaches based on nonlinear forward models counting the beam polychromaticity show great potential for giving accurate fraction images.
This work proposes a full-spectral Bayesian reconstruction approach which allows the reconstruction of high quality fraction images from ordinary polychromatic measurements. This approach is based on a Gaussian noise model with unknown variance assigned directly to the projections without taking negative-log. Referring to Bayesian inferences, the decomposition fractions and observation variance are estimated by using the joint maximum a posteriori (MAP) estimation method. Subject to an adaptive prior model assigned to the variance, the joint estimation problem is then simplified into a single estimation problem. It transforms the joint MAP estimation problem into a minimization problem with a nonquadratic cost function. To solve it, the use of a monotone conjugate gradient algorithm with suboptimal descent steps is proposed.
The performance of the proposed approach is analyzed with both simulated and experimental data. The results show that the proposed Bayesian approach is robust to noise and materials. It is also necessary to have the accurate spectrum information about the source-detector system. When dealing with experimental data, the spectrum can be predicted by a Monte Carlo simulator. For the materials between water and bone, less than 5% separation errors are observed on the estimated decomposition fractions.
The proposed approach is a statistical reconstruction approach based on a nonlinear forward model counting the full beam polychromaticity and applied directly to the projections without taking negative-log. Compared to the approaches based on linear forward models and the BHA correction approaches, it has advantages in noise robustness and reconstruction accuracy.
双能计算机断层扫描（DECT）使得无需分割即可获得两种基础物质分数成为可能。一个是软组织等效水分数，另一个是硬物质等效骨分数。实际的 DECT 测量通常使用多色 X 射线束获得。现有的基于线性正向模型的重建方法不考虑光束多色性，无法估计正确的分解分数，从而导致束硬化伪影（BHA）。现有的 BHA 校正方法要么需要参考校准测量，要么受到负对数预处理和水和骨分离问题的不良条件引起的噪声放大的影响。为了克服这些问题，基于考虑光束多色性的非线性正向模型的统计 DECT 重建方法显示出提供准确分数图像的巨大潜力。
本工作提出了一种全谱贝叶斯重建方法，该方法允许从普通多色测量中重建高质量的分数图像。该方法基于具有未知方差的高斯噪声模型，该方差直接分配给投影，而无需取负对数。参考贝叶斯推断，通过使用联合最大后验（MAP）估计方法，估计分解分数和观测方差。在分配给方差的自适应先验模型的约束下，然后将联合估计问题简化为单个估计问题。它将联合 MAP 估计问题转换为具有非二次代价函数的最小化问题。为了解决这个问题，提出了使用具有次优下降步骤的单调共轭梯度算法。
使用模拟和实验数据对所提出方法的性能进行了分析。结果表明，所提出的贝叶斯方法对噪声和材料具有鲁棒性。还需要具有源探测器系统的准确光谱信息。在处理实验数据时，可以通过蒙特卡罗模拟器预测光谱。对于水和骨之间的材料，在估计的分解分数上观察到小于 5%的分离误差。
所提出的方法是一种基于考虑全光束多色性的非线性正向模型的统计重建方法，并直接应用于投影，而无需取负对数。与基于线性正向模型的方法和 BHA 校正方法相比，它在噪声鲁棒性和重建精度方面具有优势。
