Canonical polyadic decomposition (CPD) of multi-subject complex-valued fMRI data can be used to provide spatially and temporally shared components among groups with both magnitude and phase information. However, the CPD model is not well formulated due to the large subject variability in the spatial and temporal modalities, as well as the high noise level in complex-valued fMRI data. Considering that the shift-invariant CPD can model temporal variability across subjects, we propose to further impose a phase sparsity constraint on the shared spatial maps to denoise the complex-valued components and to model the inter-subject spatial variability as well. More precisely, subject-specific time delays are first estimated for the complex-valued shared time courses in the framework of real-valued shift-invariant CPD. Source phase sparsity is then imposed on the complex-valued shared spatial maps. A smoothed l0 norm is specifically used to reduce voxels with large phase values after phase de-ambiguity based on the small phase characteristic of BOLD-related voxels. The results from both the simulated and experimental fMRI data demonstrate improvements of the proposed method over three complex-valued algorithms, namely, tensor-based spatial ICA, shift-invariant CPD and CPD without spatiotemporal constraints. When comparing with a real-valued algorithm combining shift-invariant CPD and ICA, the proposed method detects 178.7% more contiguous task-related activations.

中文翻译：

---

具有相位稀疏约束的复值多主体 fMRI 数据的移位不变规范多元分解。

多主体复值 fMRI 数据的规范多元分解 (CPD) 可用于在具有幅度和相位信息的组之间提供空间和时间共享的组件。然而，由于空间和时间模式的巨大主体可变性，以及复值 fMRI 数据中的高噪声水平，CPD 模型没有很好地制定。考虑到平移不变 CPD 可以模拟跨学科的时间可变性，我们建议进一步对共享空间图施加相位稀疏约束，以对复值分量进行去噪，并对学科间的空间可变性进行建模。更准确地说，首先在实值平移不变 CPD 框架中估计复值共享时间课程的特定主题时间延迟。然后将源相位稀疏性强加到复值共享空间图上。基于 BOLD 相关体素的小相位特性，平滑的 l0 范数专门用于在相位去模糊后减少具有大相位值的体素。模拟和实验 fMRI 数据的结果证明了所提出的方法对三种复值算法的改进，即基于张量的空间 ICA、平移不变 CPD 和无时空约束的 CPD。与结合平移不变 CPD 和 ICA 的实值算法相比，所提出的方法检测到 178.7% 的连续任务相关激活。基于 BOLD 相关体素的小相位特性，平滑的 l0 范数专门用于在相位去模糊后减少具有大相位值的体素。模拟和实验 fMRI 数据的结果证明了所提出的方法对三种复值算法的改进，即基于张量的空间 ICA、平移不变 CPD 和无时空约束的 CPD。与结合平移不变 CPD 和 ICA 的实值算法相比，所提出的方法检测到 178.7% 的连续任务相关激活。基于 BOLD 相关体素的小相位特性，平滑的 l0 范数专门用于在相位去模糊后减少具有大相位值的体素。模拟和实验 fMRI 数据的结果证明了所提出的方法对三种复值算法的改进，即基于张量的空间 ICA、平移不变 CPD 和无时空约束的 CPD。与结合平移不变 CPD 和 ICA 的实值算法相比，所提出的方法检测到 178.7% 的连续任务相关激活。