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.

翻译：本文介绍了一种高效的多线性非参数（基于核的）逼近框架，用于数据回归和插补，以及其在动态磁共振成像（dMRI）中的应用。假定数据特征在或接近嵌入再生核希尔伯特空间中的平滑流形中。标志点用于通过线性逼近块来简洁描述特征点云，这些逼近块模仿了光滑流形的切空间概念。多线性模型实现了降维，使计算高效，并提取数据模式及其几何形状，无需任何训练数据或额外信息。在严重欠采样的dMRI数据上进行的数值测试表明，与前任、流行的数据建模方法以及最近的张量和深图像先验方案相比，所提出的方法在效率和准确性方面有着显著的改进。