标题： 对数欧几里得框架用于平滑的大脑连接轨迹 显示英文标题

标题： Log-Euclidean Frameworks for Smooth Brain Connectivity Trajectories

摘要： 大脑通常从网络角度进行研究，其中功能活动使用功能性磁共振成像(fMRI)来评估预定义神经区域之间的连接性。 功能连接性可以通过随时间计算的相关矩阵表示，其中每个矩阵捕获不同区域在滑动窗口内的平均fMRI信号之间的皮尔逊相关性。 我们引入了几种对数-欧几里得黎曼框架，用于构建功能脑连接轨迹的平滑近似。 将动态功能连接表示为全秩相关矩阵的时间序列，我们利用最近的对数-欧几里得微分同胚理论，在实践中将这些轨迹映射到欧几里得空间，使得多项式回归成为可能。 将回归曲线拉回，确保每个估计点保持为有效的相关矩阵，从而实现原始脑连接动态的平滑、可解释且几何一致的近似。 在fMRI导出的连接轨迹上的实验展示了我们方法的几何一致性和计算效率。 显示英文摘要

摘要： The brain is often studied from a network perspective, where functional activity is assessed using functional Magnetic Resonance Imaging (fMRI) to estimate connectivity between predefined neuronal regions. Functional connectivity can be represented by correlation matrices computed over time, where each matrix captures the Pearson correlation between the mean fMRI signals of different regions within a sliding window. We introduce several Log-Euclidean Riemannian framework for constructing smooth approximations of functional brain connectivity trajectories. Representing dynamic functional connectivity as time series of full-rank correlation matrices, we leverage recent theoretical Log-Euclidean diffeomorphisms to map these trajectories in practice into Euclidean spaces where polynomial regression becomes feasible. Pulling back the regressed curve ensures that each estimated point remains a valid correlation matrix, enabling a smooth, interpretable, and geometrically consistent approximation of the original brain connectivity dynamics. Experiments on fMRI-derived connectivity trajectories demonstrate the geometric consistency and computational efficiency of our approach.