论文标题
内核双线性建模用于重建流形的数据：动态MRI情况
Kernel Bi-Linear Modeling for Reconstructing Data on Manifolds: The Dynamic-MRI Case
论文作者
论文摘要
本文建立了一个基于内核的框架，用于重建流形的数据，该框架量身定制，以适合动态 - （d）MRI-DATA恢复问题。所提出的方法利用了歧管的简单切线空间几何形状在再现核希尔伯特空间中，并遵循经典的内核 - 透明参数，以形成数据恢复任务作为双线性反向问题。拟议的方法与主流方法背道而驰，不使用训练数据，不采用图形laplacian矩阵来惩罚优化任务，不使用昂贵的（内核）预示步骤将特征点映射到输入空间，并利用复杂价值值值的核电函数来说明K-Space数据。该框架在合成生成的DMRI数据上进行了验证，其中与最先进的方案进行了比较突出了所提出方法在数据重新发现问题中的丰富潜力。
This paper establishes a kernel-based framework for reconstructing data on manifolds, tailored to fit the dynamic-(d)MRI-data recovery problem. The proposed methodology exploits simple tangent-space geometries of manifolds in reproducing kernel Hilbert spaces and follows classical kernel-approximation arguments to form the data-recovery task as a bi-linear inverse problem. Departing from mainstream approaches, the proposed methodology uses no training data, employs no graph Laplacian matrix to penalize the optimization task, uses no costly (kernel) pre-imaging step to map feature points back to the input space, and utilizes complex-valued kernel functions to account for k-space data. The framework is validated on synthetically generated dMRI data, where comparisons against state-of-the-art schemes highlight the rich potential of the proposed approach in data-recovery problems.
