Fast alternating projection methods for constrained tomographic reconstruction.
Fast alternating projection methods for constrained tomographic reconstruction.
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DOI：
10.1371/journal.pone.0172938
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发表时间：
2017
期刊：
影响因子：
3.7
通讯作者：
Jin M
中科院分区：
文献类型：
--
作者：
Liu L;Han Y;Jin M
交替投影算法易于实现，并且对于大规模复杂优化问题有效，例如 X 射线计算机断层扫描 (CT) 的约束重建。典型的方法是使用凸集投影 (POCS) 来保证数据保真度，使用非负约束结合总变差 (TV) 最小化（所谓的 TV-POCS）来进行稀疏视图 CT 重建。然而，此类方法依赖于经验选择的参数来进行令人满意的重建，并且通常速度较慢且缺乏收敛分析。在这项工作中，我们使用凸可行性集方法来解决与 TV-POCS 相关的问题，并提出了一个使用完全顺序交替投影或 POCS (FS-POCS) 的框架来寻找有界 TV 函数、有界数据保真度误差和非负性的凸约束的交集的解决方案。 FS-POCS 背后的基本原理是约束目标函数的数学最优解可能不是物理最优解。将约束重建分解为几个可行集的交集可以导致更快的收敛和以物理有意义的方式更好地量化重建参数，而不是通过试错的经验方式。此外，对于大规模优化问题，通常采用一阶方法。不仅导出了基于梯度的方法的收敛条件，而且还使用了原始对偶混合梯度（PDHG）方法来实现有界TV的快速收敛。使用数字体模和伪真实 CT 数据对新提出的 FS-POCS 与 TV-POCS 和另一种凸可行性投影方法 (CPTV) 进行评估和比较，以显示其在重建速度、图像质量和量化方面的优越性能。
The alternating projection algorithms are easy to implement and effective for large-scale complex optimization problems, such as constrained reconstruction of X-ray computed tomography (CT). A typical method is to use projection onto convex sets (POCS) for data fidelity, nonnegative constraints combined with total variation (TV) minimization (so called TV-POCS) for sparse-view CT reconstruction. However, this type of method relies on empirically selected parameters for satisfactory reconstruction and is generally slow and lack of convergence analysis. In this work, we use a convex feasibility set approach to address the problems associated with TV-POCS and propose a framework using full sequential alternating projections or POCS (FS-POCS) to find the solution in the intersection of convex constraints of bounded TV function, bounded data fidelity error and non-negativity. The rationale behind FS-POCS is that the mathematically optimal solution of the constrained objective function may not be the physically optimal solution. The breakdown of constrained reconstruction into an intersection of several feasible sets can lead to faster convergence and better quantification of reconstruction parameters in a physical meaningful way than that in an empirical way of trial-and-error. In addition, for large-scale optimization problems, first order methods are usually used. Not only is the condition for convergence of gradient-based methods derived, but also a primal-dual hybrid gradient (PDHG) method is used for fast convergence of bounded TV. The newly proposed FS-POCS is evaluated and compared with TV-POCS and another convex feasibility projection method (CPTV) using both digital phantom and pseudo-real CT data to show its superior performance on reconstruction speed, image quality and quantification.