空间源相位约束下完备复数fMRI数据的稀疏表示

Studies in brain sciences have become a major focus over the past five years. Functional magnetic resonance imaging (fMRI) has been widely used in the studies due to its non-invasive nature and high spatial resolution. More specifically, fMRI is very suitable for early diagnosis of brain diseases, and has achieved promising results in detecting biomarkers for brain diseases such as schizophrenia and Alzheimer's disease. However, one problem is that the results of different fMRI studies varied considerably. The complete fMRI data is a complex-valued data set. Although the phase data has lower energy, it contains unique brain function information and can be more informative than the magnitude data. Existing methods have validated the benefits of using additional phase data, and have successfully extracted from the complex-valued fMRI data brain regions that cannot be steadily extracted from the magnitude-only fMRI data, indicating that the utilization rate of fMRI brain information influences the variation of research results. However, the data reduction stage of the existing analyzing methods such as independent component analysis for complex-valued fMRI data results in loss of the brain information and the incomplete extraction of brain regions. In addition, the existing methods have not utilized the spatial sparsity that is found to be in line with the intrinsic characteristic of brain activation. Sparse representation can not only use lossless fMRI brain information since no data compression is required, but also well describe the spatial sparsity of fMRI data. Unfortunately, the existing complex-valued sparse representation methods cannot use the unique characteristics of complex-valued fMRI data, thus it is difficult for these methods to obtain the optimal performance in analyzing complex-valued fMRI data. To this end, this proposal aims to establish a framework for sparse representation of complete complex-valued fMRI data. The unique spatial source phase characteristic of complex-valued fMRI data is used as constraints to solve the key problems of the sparse representation of complex-valued fMRI data. The proposed methods are to be evaluated using resting-state complex-valued fMRI data from schizophrenia patients and healthy controls. This proposal promises to extract more complete components for developing high-quality biomarkers, to improve the stability of analysis results and the accuracy for classifying schizophrenia patients and healthy controls, and to extend to researches on other brain diseases such as Alzheimer's disease. Therefore, this proposal can contribute to the brain science research in China.

功能磁共振成像（fMRI）适于脑疾病的早期诊断，已在脑疾病标志物检测方面取得了积极成果，但不同研究之间的结果变异较大。完备fMRI数据是复数。相位数据能量极低，但含有幅值数据所没有的脑信息。现有方法从复数fMRI数据中成功提取了从幅值数据中不能稳定提取的脑区，表明fMRI脑信息的利用率是影响结果变异的因素。然而，现有复数fMRI分析方法如独立成分分析的数据压缩环节导致脑信息利用不完整，抽取的脑区有缺失，并且没有利用更符合脑激活特点的稀疏性。稀疏表示方法无需数据压缩，又适于刻画信号的稀疏性，但现有的复数稀疏表示方法不能利用fMRI的独有特性，难以获得最优性能。为此，本项目拟建立复数fMRI数据分析的稀疏表示框架，以复数数据特有的空间源相位特性为约束，解决完备复数fMRI数据稀疏表示的关键问题。本项目能提取更完整的疾病标志物，提高分析结果稳定性，提升脑疾病分类准确率，为我国脑科学研究作出贡献。

疾病标志物提取的稳定性是影响fMRI用于脑疾病诊疗的关键。本项目通过利用无压缩的完整复数fMRI数据以及脑激活的稀疏性特点提供解决方案；在复数ICA之外，为复数fMRI分析建立了一套新的数据驱动方法——复数稀疏表示。重要结果如下：（1）针对复数fMRI数据的空间稀疏性刻画，提出了源相位为主幅值为辅的联合刻画方法，以及平滑L0、L1-L2、Lp(0<p≤1)范数等约束方法，适于不同复数fMRI数据的稀疏建模。（2）针对稀疏约束参数的自适应选取，提出了稀疏阈值设定的源相位比例法，在迭代更新过程中仅对源相位最大的小部分体素进行稀疏化，保留了更多的有用体素。（3）针对单被试复数fMRI数据的稀疏表示，提出了实数域实部-虚部联合、复数域秩一矩阵逼近等两类框架，提取了仅用幅值fMRI数据难以稳定提取的脑区（如ACC）。（4）针对多被试复数fMRI数据的稀疏表示，提出了源相位稀疏约束的移不变CPD算法，比幅值fMRI数据多提取了178.7%的任务相关体素；提出了多被试幅值fMRI数据的稀疏约束低秩Tucker算法，发现了核张量空时特征在被试细分类中的结构优势。（5）针对空间源相位（SSP）信息挖掘，提出了一种病人-健康人方差差异法，将SSP组间差异的敏感度提升至幅值的300倍；构建了3D-CNN分类网络SSPNet，分类精度和可解释性显著优于幅值。已发表期刊论文10篇、会议论文8篇（SCI 9篇、EI 9篇），其中在Medical Image Analysis、IEEE Transactions on Medical Imaging等领域顶刊发表第一标注长文4篇；申请发明专利13项，已授权6项；培养博士生5人、硕士生6人；荣获校科技成果（前沿及转化）二等奖1项；在GitHub公开软件包2项；参加ICASSP等国际会议8人次。