Rehfeld Niklas, Alber Markus
Sektion für Biomedizinische Physik, Universitätsklinikum Tübingen, Hoppe-Seyler-Str 3, 72076 Tübingen, Germany.
Med Phys. 2006 Sep;33(9):3498-507. doi: 10.1118/1.2239165.
Monte Carlo (MC) simulations in positron emission tomography (PET) play an important role in detector modeling and algorithm testing. Whereas the simulations are widely used in a forward projection manner to accomplish this task, ideally they should be included into the reconstruction process itself. It is therefore desirable to investigate the convergence properties and the propagation of MC noise of these kinds of reconstruction algorithms. MC simulations were integrated into the maximum likelihood expectation maximization (ML-EM) algorithm in two different ways. In the full matrix approach the system matrix was calculated by running MC simulations, including scatter. This matrix was used in both the projector and the backprojector. In the dual matrix (DM) approach, MC simulations were used to incorporate scatter in the projector, whereas the backprojector only comprised attenuation. Repeated reconstructions with different MC seeds allowed a statistical analysis of the error at each iteration step and made it possible to investigate separately the propagation of the MC noise that was introduced by the sinogram, by the projector, and by the matrix. Both approaches resulted in similar images, but the DM approach with unmatched projector and backprojector yielded a faster initial convergence when compared to the ideal full matrix approach. The analysis of the noise sources for the modeled single ring scanner in full matrix reconstruction showed that the noise introduced by the matrix became comparable to the noise introduced by the sinogram when using a matrix that was simulated with 10,000 emissions/voxel.
正电子发射断层扫描（PET）中的蒙特卡罗（MC）模拟在探测器建模和算法测试中发挥着重要作用。虽然这些模拟广泛用于前向投影方式来完成此任务，但理想情况下，它们应纳入重建过程本身。因此，研究这类重建算法的收敛特性和MC噪声的传播是很有必要的。MC模拟以两种不同方式集成到最大似然期望最大化（ML-EM）算法中。在全矩阵方法中，通过运行包括散射的MC模拟来计算系统矩阵。该矩阵用于投影仪和反投影仪。在双矩阵（DM）方法中，MC模拟用于在投影仪中纳入散射，而反投影仪仅包含衰减。使用不同的MC种子进行重复重建，可以对每个迭代步骤的误差进行统计分析，并能够分别研究由正弦图、投影仪和矩阵引入的MC噪声的传播。两种方法都得到了相似的图像，但与理想的全矩阵方法相比，投影仪和反投影仪不匹配的DM方法产生了更快的初始收敛。对全矩阵重建中建模的单环扫描仪的噪声源分析表明，当使用以10,000次发射/体素模拟的矩阵时，矩阵引入的噪声与正弦图引入的噪声相当。
