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Low-Rank Tucker-2 Model for Multi-Subject fMRI Data Decomposition With Spatial Sparsity Constraint
IEEE Transactions on Medical Imaging ( IF 10.6 ) Pub Date : 2021-10-22 , DOI: 10.1109/tmi.2021.3122226
Yue Han 1 , Qiu-Hua Lin 1 , Li-Dan Kuang 2 , Xiao-Feng Gong 1 , Fengyu Cong 3, 4 , Yu-Ping Wang 5 , Vince D. Calhoun 6
Affiliation  

Tucker decomposition can provide an intuitive summary to understand brain function by decomposing multi-subject fMRI data into a core tensor and multiple factor matrices, and was mostly used to extract functional connectivity patterns across time/subjects using orthogonality constraints. However, these algorithms are unsuitable for extracting common spatial and temporal patterns across subjects due to distinct characteristics such as high-level noise. Motivated by a successful application of Tucker decomposition to image denoising and the intrinsic sparsity of spatial activations in fMRI, we propose a low-rank Tucker-2 model with spatial sparsity constraint to analyze multi-subject fMRI data. More precisely, we propose to impose a sparsity constraint on spatial maps by using an $ \ell _{p} $ norm ( ${0}< {p}\le {1}$ ), in addition to adding low-rank constraints on factor matrices via the Frobenius norm. We solve the constrained Tucker-2 model using alternating direction method of multipliers, and propose to update both sparsity and low-rank constrained spatial maps using half quadratic splitting. Moreover, we extract new spatial and temporal features in addition to subject-specific intensities from the core tensor, and use these features to classify multiple subjects. The results from both simulated and experimental fMRI data verify the improvement of the proposed method, compared with four related algorithms including robust Kronecker component analysis, Tucker decomposition with orthogonality constraints, canonical polyadic decomposition, and block term decomposition in extracting common spatial and temporal components across subjects. The spatial and temporal features extracted from the core tensor show promise for characterizing subjects within the same group of patients or healthy controls as well.

中文翻译:

具有空间稀疏约束的多主体 fMRI 数据分解的低秩 Tucker-2 模型

Tucker 分解可以通过将多主体 fMRI 数据分解为核心张量和多因子矩阵来提供直观的总结来理解大脑功能,并且主要用于使用正交约束来提取跨时间/主体的功能连接模式。然而,由于诸如高级噪声之类的不同特征,这些算法不适用于跨受试者提取共同的空间和时间模式。受 Tucker 分解成功应用于图像去噪和 fMRI 中空间激活的内在稀疏性的启发,我们提出了一种具有空间稀疏约束的低秩 Tucker-2 模型来分析多主体 fMRI 数据。更准确地说,我们建议通过使用 $ \ell _{p} $规范( ${0}< {p}\le {1}$ ),除了通过 Frobenius 范数对因子矩阵添加低秩约束。我们使用乘法器的交替方向方法求解约束 Tucker-2 模型,并建议使用半二次分裂更新稀疏和低秩约束空间图。此外,我们从核心张量中提取除了特定于主题的强度之外的新空间和时间特征,并使用这些特征对多个主题进行分类。模拟和实验 fMRI 数据的结果验证了所提方法的改进,与四种相关算法相比,包括鲁棒 Kronecker 分量分析、具有正交性约束的 Tucker 分解、规范多元分解和块项分解,以提取跨域的公共空间和时间分量。科目。
更新日期:2021-10-22
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