标题： 一种改进的EM算法用于解决人脑约束扩散峰度成像中的最大似然估计 显示英文标题

标题： An improved EM algorithm for solving MLE in constrained diffusion kurtosis imaging of human brain

摘要： 水分子的位移分布在数学上被表征为高斯性，而不考虑势能扩散障碍和隔室。 然而，在实际情况中并非如此：大多数生物组织由细胞膜、各种细胞内和细胞外空间以及其他隔室组成，其中水的扩散被认为具有非高斯分布。 扩散峰度成像（DKI），最近被认为是敏感的生物标志物，是扩散张量成像的扩展，它量化扩散的非高斯程度。 本工作提出了DKI中最大似然估计（MLE）的有效方案：我们从信号强度的Rician噪声模型开始。 通过增加一个Von-Mises分布的潜在相位变量，Rician似然被转换为一个可处理的联合密度，而不会失去一般性。 提出了一种快速计算方法，即用于MLE的期望最大化（EM）算法。 为了保证扩散峰度的物理相关性，我们应用三元四次（TQ）参数化来利用其正性，这给峰度施加了上限。 使用Fisher-scoring方法以实现各个扩散隔室的快速收敛。 此外，我们使用障碍方法来约束峰度的下限。 所提出的估计方案在合成数据和真实数据上进行，目的是健康的人脑。 我们将该方法与其他流行方法进行了比较，结果显示出良好的性能。 显示英文摘要

摘要： The displacement distribution of a water molecular is characterized mathematically as Gaussianity without considering potential diffusion barriers and compartments. However, this is not true in real scenario: most biological tissues are comprised of cell membranes, various intracellular and extracellular spaces, and of other compartments, where the water diffusion is referred to have a non-Gaussian distribution. Diffusion kurtosis imaging (DKI), recently considered to be one sensitive biomarker, is an extension of diffusion tensor imaging, which quantifies the degree of non-Gaussianity of the diffusion. This work proposes an efficient scheme of maximum likelihood estimation (MLE) in DKI: we start from the Rician noise model of the signal intensities. By augmenting a Von-Mises distributed latent phase variable, the Rician likelihood is transformed to a tractable joint density without loss of generality. A fast computational method, an expectation-maximization (EM) algorithm for MLE is proposed in DKI. To guarantee the physical relevance of the diffusion kurtosis we apply the ternary quartic (TQ) parametrization to utilize its positivity, which imposes the upper bound to the kurtosis. A Fisher-scoring method is used for achieving fast convergence of the individual diffusion compartments. In addition, we use the barrier method to constrain the lower bound to the kurtosis. The proposed estimation scheme is conducted on both synthetic and real data with an objective of healthy human brain. We compared the method with the other popular ones with promising performance shown in the results.