谱CT图像重建的非凸原-对偶算法
Non-convex primal-dual algorithm for image reconstruction in spectral CT
摘要：
这项工作旨在开发一种算法，通过直接反演的非线性数据模型，在光谱CT图像重建。使用非线性数据模型，我们制定的图像重建问题作为一个非凸优化规划，并开发了一个非凸原对偶（NCPD）算法来解决该计划。我们设计了多个收敛条件，并进行了数值验证研究，证明NCPD算法可以解决非凸优化程序，并在适当的数据条件下，可以反演非线性数据模型。使用NCPD算法，然后，我们重建单色图像从模拟和真实数据的数值和物理幻影收购一个标准的，全扫描双能量配置。重建结果表明，NCPD算法可以准确地校正非线性射束硬化效应。此外，我们将NCPD算法应用于非标准短扫描双能量配置收集的数值和物理幻影的模拟和真实数据，并获得与标准全扫描研究相当的单色图像，从而揭示了NCPD算法在光谱CT中实现非标准扫描配置的潜力，其中现有的间接方法是有限的。
英文摘要：
The work seeks to develop an algorithm for image reconstruction by directly inverting the non-linear data model in spectral CT. Using the non-linear data model, we formulate the image-reconstruction problem as a non-convex optimization program, and develop a non-convex primal-dual (NCPD) algorithm to solve the program. We devise multiple convergence conditions and perform verification studies numerically to demonstrate that the NCPD algorithm can solve the non-convex optimization program and under appropriate data condition, can invert the non-linear data model. Using the NCPD algorithm, we then reconstruct monochromatic images from simulated and real data of numerical and physical phantoms acquired with a standard, full-scan dual-energy configuration. The result of the reconstruction studies shows that the NCPD algorithm can correct accurately for the non-linear beam-hardening effect. Furthermore, we apply the NCPD algorithm to simulated and real data of the numerical and physical phantoms collected with non-standard, short-scan dual-energy configurations, and obtain monochromatic images comparable to those of the standard, full-scan study, thus revealing the potential of the NCPD algorithm for enabling non-standard scanning configurations in spectral CT, where the existing indirect methods are limited.
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