Standard computed tomography (CT) cannot reproduce spectral information of an object. Hardware solutions include dual-energy CT which scans the object twice in different x-ray energy levels, and energy-discriminative detectors which can separate lower and higher energy levels from a single x-ray scan. In this paper, we propose a software solution and give an iterative algorithm that reconstructs an image with spectral information from just one scan with a standard energy-integrating detector. The spectral information obtained can be used to produce color CT images, spectral curves of the attenuation coefficient μ(r, E)at points inside the object, and photoelectric images, which are all valuable imaging tools in cancerous diagnosis. Our software solution requires no change on hardware of a CT machine. With the Shepp-Logan phantom, we have found that although the photoelectric and Compton components were not perfectly reconstructed, their composite effect was very accurately reconstructed as compared to the ground truth and the dual-energy CT counterpart. This means that our proposed method has an intrinsic benefit in beam hardening correction and metal artifact reduction. The algorithm is based on a nonlinear polychromatic acquisition model for x-ray CT. The key technique is a sparse representation of iterations in a framelet system. Convergence of the algorithm is studied. This is believed to be the first application of framelet imaging tools to a nonlinear inverse problem.

中文翻译：

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一种基于framelet的光谱CT迭代最大似然重建算法

标准计算机断层扫描 (CT) 无法再现物体的光谱信息。硬件解决方案包括双能 CT，它在不同的 X 射线能量水平下对物体进行两次扫描，以及可以从一次 X 射线扫描中分离出较低和较高能量水平的能量鉴别探测器。在本文中，我们提出了一种软件解决方案，并给出了一种迭代算法，该算法使用标准能量积分检测器仅通过一次扫描即可重建具有光谱信息的图像。获得的光谱信息可用于生成彩色CT图像、物体内部各点衰减系数μ(r,E)的光谱曲线和光电图像，这些都是癌症诊断中有价值的成像工具。我们的软件解决方案不需要更改 CT 机器的硬件。有了 Shepp-Logan 幻影，我们发现，虽然光电和康普顿组件没有被完美地重建，但与地面实况和双能 CT 对应物相比，它们的复合效应被非常准确地重建。这意味着我们提出的方法在光束硬化校正和金属伪影减少方面具有内在的好处。该算法基于 X 射线 CT 的非线性多色采集模型。关键技术是框架系统中迭代的稀疏表示。研究了算法的收敛性。这被认为是框架成像工具首次应用于非线性逆问题。与地面实况和双能 CT 对应物相比，它们的复合效应得到了非常准确的重建。这意味着我们提出的方法在光束硬化校正和金属伪影减少方面具有内在的好处。该算法基于 X 射线 CT 的非线性多色采集模型。关键技术是框架系统中迭代的稀疏表示。研究了算法的收敛性。这被认为是框架成像工具首次应用于非线性逆问题。与地面实况和双能 CT 对应物相比，它们的复合效应得到了非常准确的重建。这意味着我们提出的方法在光束硬化校正和金属伪影减少方面具有内在的好处。该算法基于 X 射线 CT 的非线性多色采集模型。关键技术是框架系统中迭代的稀疏表示。研究了算法的收敛性。这被认为是框架成像工具首次应用于非线性逆问题。研究了算法的收敛性。这被认为是框架成像工具首次应用于非线性逆问题。研究了算法的收敛性。这被认为是框架成像工具首次应用于非线性逆问题。