Zhang Mengxi, Zhou Jian, Niu Xiaofeng, Asma Evren, Wang Wenli, Qi Jinyi
Department of Biomedical Engineering, University of California, Davis, CA, United States of America.
Phys Med Biol. 2017 Jun 21;62(12):5114-5130. doi: 10.1088/1361-6560/aa6cdf. Epub 2017 Apr 12.
Penalized likelihood (PL) reconstruction has demonstrated potential to improve image quality of positron emission tomography (PET) over unregularized ordered-subsets expectation-maximization (OSEM) algorithm. However, selecting proper regularization parameters in PL reconstruction has been challenging due to the lack of ground truth and variation of penalty functions. Here we present a method to choose regularization parameters using a cross-validation log-likelihood (CVLL) function. This new method does not require any knowledge of the true image and is directly applicable to list-mode PET data. We performed statistical analysis of the mean and variance of the CVLL. The results show that the CVLL provides an unbiased estimate of the log-likelihood function calculated using the noise free data. The predicted variance can be used to verify the statistical significance of the difference between CVLL values. The proposed method was validated using simulation studies and also applied to real patient data. The reconstructed images using optimum parameters selected by the proposed method show good image quality visually.
惩罚似然（PL）重建已显示出相较于未正则化的有序子集期望最大化（OSEM）算法，有提高正电子发射断层扫描（PET）图像质量的潜力。然而，由于缺乏真实数据以及惩罚函数的变化，在PL重建中选择合适的正则化参数一直具有挑战性。在此，我们提出一种使用交叉验证对数似然（CVLL）函数来选择正则化参数的方法。这种新方法不需要任何关于真实图像的知识，并且可直接应用于列表模式PET数据。我们对CVLL的均值和方差进行了统计分析。结果表明，CVLL提供了使用无噪声数据计算的对数似然函数的无偏估计。预测的方差可用于验证CVLL值之间差异的统计显著性。所提出的方法通过模拟研究进行了验证，并应用于真实患者数据。使用所提出的方法选择的最佳参数重建的图像在视觉上显示出良好的图像质量。
