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This paper introduces an efficient multi-linear nonparametric (kernel-based)approximation framework for data regression and imputation, and its applicationto dynamic magnetic-resonance imaging (dMRI). Data features are assumed toreside in or close to a smooth manifold embedded in a reproducing kernelHilbert space. Landmark points are identified to describe concisely the pointcloud of features by linear approximating patches which mimic the concept oftangent spaces to smooth manifolds. The multi-linear model effectsdimensionality reduction, enables efficient computations, and extracts datapatterns and their geometry without any training data or additionalinformation. Numerical tests on dMRI data under severe under-samplingdemonstrate remarkable improvements in efficiency and accuracy of the proposedapproach over its predecessors, popular data modeling methods, as well asrecent tensor-based and deep-image-prior schemes.

Multi-Linear Kernel Regression and Imputation in Data Manifolds