Kernel Bi-Linear Modeling for Reconstructing Data on Manifolds: The Dynamic-MRI Case
| Autor: | Gaurav N. Shetty, Gesualdo Scutari, Konstantinos Slavakis, Ukash Nakarmi, Leslie Ying |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
FOS: Computer and information sciences
Computer Science - Machine Learning Computer science Computer Vision and Pattern Recognition (cs.CV) Computer Science - Computer Vision and Pattern Recognition Bilinear interpolation Machine Learning (stat.ML) 02 engineering and technology Space (mathematics) Machine Learning (cs.LG) Matrix (mathematics) Kernel (linear algebra) symbols.namesake Statistics - Machine Learning Simple (abstract algebra) FOS: Electrical engineering electronic engineering information engineering 0202 electrical engineering electronic engineering information engineering Training set Image and Video Processing (eess.IV) Hilbert space 020206 networking & telecommunications Electrical Engineering and Systems Science - Image and Video Processing Inverse problem Manifold Kernel (statistics) symbols 020201 artificial intelligence & image processing Laplacian matrix Algorithm |
| Zdroj: | EUSIPCO |
| DOI: | 10.23919/eusipco47968.2020.9287848 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|