MAP reconstruction from spatially correlated PET data
MAP reconstruction from spatially correlated PET data
复制标题
DOI：
10.1109/tns.2003.817943
复制
发表时间：
2003-10-01
影响因子：
1.8
通讯作者：
Bouman, CA
中科院分区：
文献类型：
--
作者：
Alessio, A;Sauer, K;Bouman, CA
高灵敏度 3-D PET 数据通常会重新组合成 2-D 数据集，以减少重建的计算时间。在重新分类之前需要针对衰减、意外、散射和死区时间效应预先校正 3D 数据，并且重新分类过程本身会改变数据的统计数据。本文提出了一种查找和使用傅立叶重组 (FORE) 数据统计数据的方法。特别是，利用 FORE 的空间域表示，我们找到了近似协方差矩阵。我们还使用 2-D 正向投影仪对重新分档数据的平均值进行了改进的估计，更准确地表示了 FORE 对原始 3-D PET 测量的影响。为了合并相关信息，我们将图像条件下的数据建模为低阶马尔可夫场。该模型基于相关二维 PET 数据的对数似然的二次近似。然后将依赖关系纳入一种新颖的最大后验 (MAP) 二维重建方法中。初步结果表明，与基于泊松的 MAP 方法相比，该方法通过参考图像提供了适度的 MSE 改进。结果还表明，仅使用改进的均值可显着改善 FORE 数据的重建效果。
High sensitivity 3-D PET data is often rebinned into 2-D data sets in order to reduce the computation time of reconstructions. The need to precorrect the 3-D data for attenuation, accidentals, scatter, and deadtime effects before rebinning along with the rebinning process itself changes the statistics of the data. This paper presents an approach for finding and using the statistics of Fourier rebinned (FORE) data. In particular, utilizing a space domain representation of FORE, we find the approximate covariance matrix. We also derive an improved estimate of the mean of the rebinned data with a 2-D forward projector that more accurately represents the effect of FORE on the original 3-D PET measurements. In order to incorporate dependent information, we model the data conditioned on the image as a low-order Markov field. This model is based on a quadratic approximation of the log-likelihood of dependent 2-D PET data. The dependence relationship is then incorporated into a novel maximum a posteriori (MAP) 2-D reconstruction method. Initial results show that this method offers modest MSE improvements with a reference image over Poisson-based MAP methods. Results also reveal that the use of only the improved mean leads to significant improvements in reconstructions from FORE data.