一类非均匀有界回归混合模型的建模及在fMRI时间序列聚类中的应用

Studying how to accurately extract brain activity regions from fMRI time-series is of great significance and important in cognitive neuroscience community. The purpose of this project is to derive various nonsymmetric bounded regression mixture models (RMM) which merge multiple multivariate probability distributions as well as their applications on fMRI time-series clustering, including the following problems：(1) According to the probability distribution's own peculiarities, this study will present a series of new nonsymmetric probability density functions which group multiple multivariate probability distributions. (2) The project will construct their corresponding RMM in terms of these nonsymmetric probability density functions to describe high dimension observation data fMRI time-series, so that we can consider the space and time relativities between neighbor voxels from the point of view of statistical theory. (3) By introducing the frequency domain and time domain features, the proposed nonsymmetric bounded RMM can detect the regions of significant activation inside the brain in an accurate manner and solve the potential delay problems between hemodynamic response signal and cognitive stimuli signal. (4) Research group will present some nonsymmetric bounded RMM algorithms which base on Markov random field, mean template or other regularization terms. (5) The study may utilize the space- alternating generalized expectation-maximization algorithm to estimate the parameters of proposed models. (6) The project will discuss the proposed mixture models' properties of uniqueness, identifiability, and investigate the convergence of objective functions. It can be expected that new methods discussed in this project have very important science values and great clinical applications to the segmentation of blurred medical images as well as the clustering of fMRI time-series.

从fMRI时间序列中精确检测功能激活区在认知神经研究领域极具研究价值。本项目旨在开展一类非均匀有界回归混合模型(RMM)的建模及在fMRI时间序列聚类中应用的研究，解决(1)寻找有效方法生成一类融合任意多个、多变量概率分布的非均匀概率密度函数；(2)构造服从这些函数的非均匀有界RMM描述高维观测数据fMRI时间序列，从统计理论的视角考虑邻域体素间的相关性；(3)构造联合频域与时域特征度量的非均匀有界RMM，在脑血液动力学响应信号与功能认知任务刺激之间存在不特定延迟时能达到精准检测脑激活区的目的；(4)研究基于Markov随机场、均值模板和其它正则项的非均匀有界RMM；(5)研究用空间交替广义期望最大化法优化模型参数；(6)研究非均匀有界RMM表达式的唯一性、可辨识性及目标函数的收敛性。项目研究将对区域难以界定医学图像分割及低信噪比fMRI时间序列聚类的理论研究和临床应用具有重要的学术价值。

涉及认知神经科学的医疗诊断常采用各种脑成像技术生成的时间序列进行和大脑神经活动相关的决策研究，fMRI技术就是这样一种通过大脑血氧水平依赖(BOLD)信号呈现脑区神经元活动状态的成像方法，这些活动状态被认为与精神分裂症、抑郁症、癫痫、阿尔茨海默等疾病有关，按照项目研究计划，重点研究了一类非均匀有界回归混合模型(RMM)的建模及在fMRI时间序列聚类中应用的研究，主要包括：(1)开展了构造一类新的非均匀概率密度函数，以及服从这些函数的非均匀有限混合模型的研究；(2)开展了融合多概率分布的非均匀有界回归混合模型fMRI时间序列聚类算法的研究；(3)开展了基于噪声鲁棒的非对称混合模型的fMRI时间序列聚类分析算法(RSMM-MRF)的研究；(4)开展了联合频域和时域特征的非均匀有界回归混合模型fMRI时间序列脑激活区提取算法的研究；(5) 开展了对非均匀有界回归混合模型的可辨识性、唯一性、目标函数的收敛性研究。项目对非均匀有界回归混合模型、特别是组合了频域与时域联合特征的非均匀有界回归混合模型的研究有望比用已有的广义线性模型、高斯回归混合模型在fMRI功能认知任务数据分析领域具有更广泛使用的价值。