Wolfson Molecular Imaging Centre, MAHSC, University of Manchester, Manchester, UK.
Phys Med Biol. 2013 Aug 7;58(15):5061-83. doi: 10.1088/0031-9155/58/15/5061. Epub 2013 Jul 8.
Recent studies have demonstrated the benefits of a resolution model within iterative reconstruction algorithms in an attempt to account for effects that degrade the spatial resolution of the reconstructed images. However, these algorithms suffer from slower convergence rates, compared to algorithms where no resolution model is used, due to the additional need to solve an image deconvolution problem. In this paper, a recently proposed algorithm, which decouples the tomographic and image deconvolution problems within an image-based expectation maximization (EM) framework, was evaluated. This separation is convenient, because more computational effort can be placed on the image deconvolution problem and therefore accelerate convergence. Since the computational cost of solving the image deconvolution problem is relatively small, multiple image-based EM iterations do not significantly increase the overall reconstruction time. The proposed algorithm was evaluated using 2D simulations, as well as measured 3D data acquired on the high-resolution research tomograph. Results showed that bias reduction can be accelerated by interleaving multiple iterations of the image-based EM algorithm solving the resolution model problem, with a single EM iteration solving the tomographic problem. Significant improvements were observed particularly for voxels that were located on the boundaries between regions of high contrast within the object being imaged and for small regions of interest, where resolution recovery is usually more challenging. Minor differences were observed using the proposed nested algorithm, compared to the single iteration normally performed, when an optimal number of iterations are performed for each algorithm. However, using the proposed nested approach convergence is significantly accelerated enabling reconstruction using far fewer tomographic iterations (up to 70% fewer iterations for small regions). Nevertheless, the optimal number of nested image-based EM iterations is hard to be defined and it should be selected according to the given application.
最近的研究表明，在迭代重建算法中采用分辨率模型有助于解决重建图像空间分辨率降低的问题。然而，与不使用分辨率模型的算法相比，这些算法的收敛速度较慢，因为需要额外解决图像反卷积问题。在本文中，评估了一种最近提出的算法，该算法在基于图像的期望最大化（EM）框架内将层析和图像反卷积问题分离。这种分离很方便，因为可以将更多的计算资源用于图像反卷积问题，从而加速收敛。由于求解图像反卷积问题的计算成本相对较小，因此多次基于图像的 EM 迭代不会显著增加整体重建时间。该算法使用 2D 模拟以及在高分辨率研究断层扫描仪上获取的测量 3D 数据进行了评估。结果表明，通过交错多次基于图像的 EM 算法迭代来解决分辨率模型问题，并使用单个 EM 迭代来解决层析问题，可以加速降低偏差。对于位于成像物体中高对比度区域之间边界处的体素以及小感兴趣区域，观察到了显著的改进，因为这些区域的分辨率恢复通常更具挑战性。当为每个算法执行最佳迭代次数时，与通常执行的单个迭代相比，使用所提出的嵌套算法观察到的差异较小。然而，使用所提出的嵌套方法可以显著加速收敛，从而使用更少的层析迭代进行重建（对于小区域，减少多达 70%的迭代次数）。然而，很难定义最优的嵌套基于图像的 EM 迭代次数，应该根据给定的应用进行选择。
