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.

本文介绍了一种基于核的高效多线性非参数逼近框架，应用于动态磁共振成像（dMRI）的数据回归和插值。该多线性模型具有降维、高效计算和提取数据模式和几何形状等特点，在严重欠采样的 dMRI 数据测试中较之以往的方法，包括流行的数据建模方法及最近的张量和深度图像先验方案，均表现出了显著的效率和准确性的提升。