Nuyts J, Michel C, Dupont P
Department of Nuclear Medicine, K.U. Leuven, Belgium.
IEEE Trans Med Imaging. 2001 May;20(5):365-75. doi: 10.1109/42.925290.
The maximum-likelihood (ML) expectation-maximization (EM) [ML-EM] algorithm is being widely used for image reconstruction in positron emission tomography. The algorithm is strictly valid if the data are Poisson distributed. However, it is also often applied to processed sinograms that do not meet this requirement. This may sometimes lead to suboptimal results: streak artifacts appear and the algorithm converges toward a lower likelihood value. As a remedy, we propose two simple pixel-by-pixel methods [noise equivalent counts (NEC)-scaling and NEC-shifting] in order to transform arbitrary sinogram noise into noise which is approximately Poisson distributed (the first and second moments of the distribution match those of the Poisson distribution). The convergence speed associated with both transformation methods is compared, and the NEC-scaling method is validated with both simulations and clinical data. These new methods extend the ML-EM algorithm to a general purpose nonnegative reconstruction algorithm.
最大似然（ML）期望最大化（EM）[ML-EM]算法正广泛应用于正电子发射断层扫描中的图像重建。如果数据呈泊松分布，该算法严格有效。然而，它也经常应用于不满足此要求的处理后的正弦图。这有时可能导致次优结果：出现条纹伪影，并且算法收敛到较低的似然值。作为一种补救措施，我们提出了两种简单的逐像素方法[噪声等效计数（NEC）缩放和NEC移位]，以便将任意正弦图噪声转换为近似泊松分布的噪声（分布的一阶和二阶矩与泊松分布的匹配）。比较了与两种变换方法相关的收敛速度，并通过模拟和临床数据验证了NEC缩放方法。这些新方法将ML-EM算法扩展为一种通用的非负重建算法。
