基于耦合张量分解的高维多被试复数fMRI数据分析

In recent years, studies in brain sciences have attracted worldwide attention. Functional magnetic resonance imaging (fMRI) with the advantages of non-invasive nature and high spatial resolution, has been widely applied in brain science research. In fact, multi-subject fMRI data are intrinsically high-dimensional (i.e., five-ways tensor) and complex-valued data. However, the majority of studies reshape the data into three-ways tensor or matrix, and only focus on magnitude-only data analysis. Thus, this leads to the analysis accuracy loss and deficient brain functional information exploitation. Making full use of the high-dimensional structure of complex-valued fMRI data, can help to extract more complete and practical brain functional characteristics. Nevertheless, when we analyze the high-dimensional multi-subject complex-valued fMRI data, we will face the following three problems: 1) the scan-acquired whole fMRI data contain many useless out-brain voxels (about 2/3 of whole voxels), and the number of in-brain voxels of each slice is different; 2) large inter-subject variability; 3) high-noisy nature of complex-valued fMRI data. This proposal intends to utilize coupled tensor decomposition to give the solutions for the above problems. Coupled tensor decomposition model is very flexible. It can not only depict high-dimensional data structure, but also jointly decompose different tensors, allowing differences among different slice tensors. To this end, this proposal firstly aims to establish coupled high-dimensional tensorization models of high-dimensional multi-subject complex-valued fMRI in-brain data. Secondly, coupled tensor decomposition with spatiotemporal constraints are to be proposed. Thirdly, efficient model order estimation methods are to be proposed by jointly exploiting both the statistical and structural properties of the data. Finally, based on the resting-state fMRI data consisting of schizophrenia patients (SZs) and healthy controls (HCs), the proposal intends to explore the brain functional information of shared complex-valued spatiotemporal components, and improve the classification accuracy of SZs and HCs. Our proposed methods can be straightforwardly extended to other brain disease studies, and contribute to our Chinese brain science research.

功能磁共振成像（fMRI）是脑科学研究的重要手段之一。多被试fMRI本质上是高维、复数数据，但分析时一般将其低维化且只分析幅值数据，导致分析精度损失及脑信息利用不全。充分利用复数fMRI数据的高维结构，有助于提取更完整、更切实际的脑功能特性。然而，高维多被试复数fMRI数据存在脑外无用数据多（约占全部扫描数据的2/3），脑内各切片体素数目不同、多被试空时差异、复数数据噪声高等问题。为此，本项目拟基于耦合张量分解给出解决方案。耦合张量分解模型灵活，既善于刻画高维数据结构，又能对不同张量进行联合分解，容许不同切片张量存在差异。本项目拟以高维多被试复数fMRI脑内数据为研究对象，建立其耦合张量化模型，提出复数空时约束的耦合张量分解算法，提出同时考虑统计和结构特性的模型阶数估计方法，挖掘复数共享空时成分的脑功能信息，提升精神分裂症的分类准确率。本项目方法易于推广到其他脑疾病，助力我国脑科学发展。

功能磁共振成像（fMRI）是脑科学研究的重要手段之一。多被试fMRI本质上是高维、复数数据，但分析时一般将其低维化且只分析幅值数据，导致分析精度损失及脑信息利用不全。充分利用复数fMRI数据的高维结构，有助于提取更完整、更切实际的脑功能特性。然而，高维多被试复数fMRI数据存在脑外无用数据多（约占全部扫描数据的2/3），脑内各切片体素数目不同、多被试空时差异大、复数数据噪声高等问题。为此，本项目开展了如下四大项研究工作。.第一，考虑到多被试fMRI数据的高维特性，构建了针对多组fMRI数据的耦合典范多因子分解(CCPD)算法模型和针对四维多被试fMRI数据的块项分解（BTD）算法模型；.第二，充分利用复数空间成分的统计独立性、稀疏性、小相位特性和正交性以及时间成分的移不变特性，提出了引入空间加权池化预处理的多被试fMRI数据约束BTD算法、空间正交约束的快速rank-(L,L,1,1)BTD算法、引入空间参考和正交约束的多组复数fMRI数据CCPD算法、采用交替秩R和秩1最小二乘更新的复数多被试fMRI约束典范多因子分解(CPD)算法、引入空间源相位稀疏约束的多被试复数fMRI数据移不变CPD算法和引入空间稀疏约束的多被试fMRI数据Tucker分解方法等，这些方法在高噪声且高被试间空时差异大的多被试复数任务态fMRI数据分离中性能显著提升；.第三，研究了快速rank-(L,L,1,1)BTD算法和加权池化压缩后的快速rank-(L,L,1,1)BTD算法中模型阶数的影响，更准确地估计模型阶数；.第四，将基于引入空间参考和正交约束的CCPD算法应用于含健康被试（HC）和精神分裂症患者（SZ）的数据分析中，发现了该方法能够获取更大的组间差异性；提出了融合复数时频特性和功能连接的疾病分类方法，获取了更优的组间差异，提升了HC和SZ的分类性能。因此，本项目方法能够获取更优的复数共享空时成分，提升了精神分裂症的分类准确率，本项目方法也易于推广到其他脑疾病，助力我国脑科学发展。