CREATIS, CNRS UMR 5220, INSERMU630, INSA-Lyon, Lyon University, 69621 Lyon, France.
IEEE Trans Med Imaging. 2010 Jul;29(7):1442-54. doi: 10.1109/TMI.2010.2048119. Epub 2010 Apr 19.
Two groups of bootstrap methods have been proposed to estimate the statistical properties of positron emission tomography (PET) images by generating multiple statistically equivalent data sets from few data samples. The first group generates resampled data based on a parametric approach assuming that data from which resampling is performed follows a Poisson distribution while the second group consists of nonparametric approaches. These methods either require a unique original sample or a series of statistically equivalent data that can be list-mode files or sinograms. Previous reports regarding these bootstrap approaches suggest different results. This work compares the accuracy of three of these bootstrap methods for 3-D PET imaging based on simulated data. Two methods are based on a unique file, namely a list-mode based nonparametric (LMNP) method and a sinogram based parametric (SP) method. The third method is a sinogram-based nonparametric (SNP) method. Another original method (extended LMNP) was also investigated, which is an extension of the LMNP methods based on deriving a resampled list-mode file by drawings events from multiple original list-mode files. Our comparison is based on the analysis of the statistical moments estimated on the repeated and resampled data. This includes the probability density function and the moments of order 1 and 2. Results show that the two methods based on multiple original data (SNP and extended LMNP) are the only methods that correctly estimate the statistical parameters. Performances of the LMNP and SP methods are variable. Simulated data used in this study were characterized by a high noise level. Differences among the tested strategies might be reduced with clinical data sets with lower noise.
两组自举方法已被提出，通过从少数数据样本中生成多个在统计上等效的数据组来估计正电子发射断层扫描 (PET) 图像的统计特性。第一组方法基于参数方法生成重采样数据，假设进行重采样的数据服从泊松分布，而第二组方法由非参数方法组成。这些方法要么需要一个唯一的原始样本，要么需要一系列在统计上等效的数据，可以是列表模式文件或正弦图。以前关于这些自举方法的报告提出了不同的结果。本工作基于模拟数据比较了这三种自举方法在 3D PET 成像中的准确性。两种方法基于唯一的文件，即基于列表模式的非参数（LMNP）方法和基于正弦图的参数（SP）方法。第三种方法是基于正弦图的非参数（SNP）方法。还研究了另一种原始方法（扩展 LMNP），它是基于从多个原始列表模式文件中抽取事件来生成重采样列表模式文件的 LMNP 方法的扩展。我们的比较基于对重复和重采样数据估计的统计矩的分析。这包括概率密度函数和阶数为 1 和 2 的矩。结果表明，基于多个原始数据的两种方法（SNP 和扩展 LMNP）是唯一能够正确估计统计参数的方法。LMNP 和 SP 方法的性能是可变的。本研究中使用的模拟数据具有高噪声水平。在具有较低噪声的临床数据集上，测试策略之间的差异可能会减少。
