论文标题
具有已知连续运动模型的ML-EM算法
ML-EM algorithm with known continuous movement model
论文作者
论文摘要
在正电子发射断层扫描中，如果不考虑，运动会导致模糊的重建。无论是已知的先验或共同估计的重建，运动模型都在连续体中越来越定义，即在离散中，例如通过差异性。目前的工作提供了一个适合处理此类模型的统计和功能分析框架。它基于时间间隔泊松点过程以及图像作为测量的图像，并允许使用已知的运动模型计算响应数据线数据的最大似然问题。解决所得的优化问题，我们得出了最大似然期望最大化（ML-EM）类型算法，该算法恢复了经典的ML-EM算法作为静态幻影的特定情况。该算法被证明是单调的，并且在低噪声方面是收敛的。模拟确认，如果忽略运动，它会正确消除将会发生的模糊。
In Positron Emission Tomography, movement leads to blurry reconstructions when not accounted for. Whether known a priori or estimated jointly to reconstruction, motion models are increasingly defined in continuum rather that in discrete, for example by means of diffeomorphisms. The present work provides both a statistical and functional analytic framework suitable for handling such models. It is based on time-space Poisson point processes as well as regarding images as measures, and allows to compute the maximum likelihood problem for line-of-response data with a known movement model. Solving the resulting optimisation problem, we derive an Maximum Likelihood Expectation Maximisation (ML-EM) type algorithm which recovers the classical ML-EM algorithm as a particular case for a static phantom. The algorithm is proved to be monotone and convergent in the low-noise regime. Simulations confirm that it correctly removes the blur that would have occurred if movement were neglected.
