  This paper introduces an efficient multi-linear nonparametric (kernel-based)
approximation framework for data regression and imputation, and its application
to dynamic magnetic-resonance imaging (dMRI). Data features are assumed to
reside in or close to a smooth manifold embedded in a reproducing kernel
Hilbert space. Landmark points are identified to describe concisely the point
cloud of features by linear approximating patches which mimic the concept of
tangent spaces to smooth manifolds. The multi-linear model effects
dimensionality reduction, enables efficient computations, and extracts data
patterns and their geometry without any training data or additional
information. Numerical tests on dMRI data under severe under-sampling
demonstrate remarkable improvements in efficiency and accuracy of the proposed
approach over its predecessors, popular data modeling methods, as well as
recent tensor-based and deep-image-prior schemes.
