Chen Buxin, Zhang Zheng, Sidky Emil Y, Xia Dan, Pan Xiaochuan
Department of Radiology, The University of Chicago, Chicago, IL 60637, United States of America.
Phys Med Biol. 2017 Nov 2;62(22):8763-8793. doi: 10.1088/1361-6560/aa8a4b.
Optimization-based algorithms for image reconstruction in multispectral (or photon-counting) computed tomography (MCT) remains a topic of active research. The challenge of optimization-based image reconstruction in MCT stems from the inherently non-linear data model that can lead to a non-convex optimization program for which no mathematically exact solver seems to exist for achieving globally optimal solutions. In this work, based upon a non-linear data model, we design a non-convex optimization program, derive its first-order-optimality conditions, and propose an algorithm to solve the program for image reconstruction in MCT. In addition to consideration of image reconstruction for the standard scan configuration, the emphasis is on investigating the algorithm's potential for enabling non-standard scan configurations with no or minimum hardware modification to existing CT systems, which has potential practical implications for lowered hardware cost, enhanced scanning flexibility, and reduced imaging dose/time in MCT. Numerical studies are carried out for verification of the algorithm and its implementation, and for a preliminary demonstration and characterization of the algorithm in reconstructing images and in enabling non-standard configurations with varying scanning angular range and/or x-ray illumination coverage in MCT.
用于多光谱（或光子计数）计算机断层扫描（MCT）中图像重建的基于优化的算法仍然是一个活跃的研究课题。MCT中基于优化的图像重建面临的挑战源于其固有的非线性数据模型，该模型可能导致一个非凸优化问题，对于此类问题，似乎不存在能够获得全局最优解的数学精确求解器。在这项工作中，基于非线性数据模型，我们设计了一个非凸优化程序，推导了其一阶最优性条件，并提出了一种算法来求解该程序以用于MCT中的图像重建。除了考虑标准扫描配置的图像重建外，重点在于研究该算法在不改变或最小化现有CT系统硬件的情况下实现非标准扫描配置的潜力，这对于降低MCT中的硬件成本、提高扫描灵活性以及减少成像剂量/时间具有潜在的实际意义。进行了数值研究以验证该算法及其实现，并初步展示和表征该算法在MCT中重建图像以及实现具有不同扫描角度范围和/或X射线照射覆盖的非标准配置方面的性能。
