Department of Radiology, Brigham and Women's Hospital-Harvard Medical School Boston, MA, USA.
Phys Med Biol. 2010 Sep 21;55(18):5341-61. doi: 10.1088/0031-9155/55/18/006. Epub 2010 Aug 24.
Tomographic reconstruction on an irregular grid may be superior to reconstruction on a regular grid. This is achieved through an appropriate choice of the image space model, the selection of an optimal set of points and the use of any available prior information during the reconstruction process. Accordingly, a number of reconstruction-related parameters must be optimized for best performance. In this work, a 3D point cloud tetrahedral mesh reconstruction method is evaluated for quantitative tasks. A linear image model is employed to obtain the reconstruction system matrix and five point generation strategies are studied. The evaluation is performed using the recovery coefficient, as well as voxel- and template-based estimates of bias and variance measures, computed over specific regions in the reconstructed image. A similar analysis is performed for regular grid reconstructions that use voxel basis functions. The maximum likelihood expectation maximization reconstruction algorithm is used. For the tetrahedral reconstructions, of the five point generation methods that are evaluated, three use image priors. For evaluation purposes, an object consisting of overlapping spheres with varying activity is simulated. The exact parallel projection data of this object are obtained analytically using a parallel projector, and multiple Poisson noise realizations of these exact data are generated and reconstructed using the different point generation strategies. The unconstrained nature of point placement in some of the irregular mesh-based reconstruction strategies has superior activity recovery for small, low-contrast image regions. The results show that, with an appropriately generated set of mesh points, the irregular grid reconstruction methods can out-perform reconstructions on a regular grid for mathematical phantoms, in terms of the performance measures evaluated.
在不规则网格上进行层析重建可能优于在规则网格上进行重建。这可以通过适当选择图像空间模型、选择最佳点集以及在重建过程中利用任何可用的先验信息来实现。因此，必须对许多与重建相关的参数进行优化，以获得最佳性能。在这项工作中，评估了一种用于定量任务的 3D 点云四面体网格重建方法。采用线性图像模型获取重建系统矩阵，并研究了五种点生成策略。使用恢复系数以及基于体素和模板的偏差和方差度量的估计值来评估，这些估计值是在重建图像的特定区域中计算得出的。对于使用体素基函数的规则网格重建，也进行了类似的分析。使用最大似然期望最大化重建算法。对于四面体重建，在评估的五种点生成方法中，有三种方法使用了图像先验。为了评估目的，模拟了一个具有不同活性的重叠球体的物体。使用平行投影仪对该物体的精确平行投影数据进行了分析，并使用不同的点生成策略对这些精确数据的多个泊松噪声实现进行了生成和重建。在一些基于不规则网格的重建策略中，点的放置不受约束，对于小的、低对比度的图像区域，具有更好的活性恢复能力。结果表明，对于数学体模，在评估的性能指标方面，使用适当生成的一组网格点，不规则网格重建方法可以优于规则网格重建方法。
