Abstract
This paper introduces an efficient multi-linear non- parametric
(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