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arXiv 2002.11885cs.LGcs.CVeess.IVstat.ML

Kernel Bi-Linear Modeling for Reconstructing Data on Manifolds: The Dynamic-MRI Case

University at Buffalo(布法罗大学);Stanford University(斯坦福大学);Purdue University(普渡大学)

Gaurav N. Shetty, Konstantinos Slavakis, Ukash Nakarmi, Gesualdo Scutari, Leslie Ying

英文摘要:

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.

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