Statistical image reconstruction (SIR) methods are studied extensively for X-ray computed tomography (CT) due to the potential of acquiring CT scans with reduced X-ray dose while maintaining image quality. However, the longer reconstruction time of SIR methods hinders their use in X-ray CT in practice. To accelerate statistical methods, many optimization techniques have been investigated. Over-relaxation is a common technique to speed up convergence of iterative algorithms. For instance, using a relaxation parameter that is close to two in alternating direction method of multipliers (ADMM) has been shown to speed up convergence significantly. This paper proposes a relaxed linearized augmented Lagrangian (AL) method that shows theoretical faster convergence rate with over-relaxation and applies the proposed relaxed linearized AL method to X-ray CT image reconstruction problems. Experimental results with both simulated and real CT scan data show that the proposed relaxed algorithm (with ordered-subsets [OS] acceleration) is about twice as fast as the existing unrelaxed fast algorithms, with negligible computation and memory overhead.

本文介绍了一种基于放松线性化增广拉格朗日(AL)方法的统计图像重建技术，该方法在交替方向方法（ADMM）的松弛参数为2时有理论加速收敛的效果，并将其应用于X射线CT图像重建问题。实验表明，相对于现有非弛張快速算法，采用所提出的放松算法（在有序子集[OS]加速下）运行速度提升了约两倍，并且计算和内存开销非常小。

快速X射线CT图像重建的松弛线性算法