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：本文提出了一种高效的多线性非参数（基于核的）逼近框架，用于数据回归与插补，并将其应用于动态磁共振成像（dMRI）。数据特征被假设位于或接近一个嵌入再生核希尔伯特空间的平滑流形中。通过识别地标点，利用线性逼近片（模拟平滑流形切空间的概念）简洁地描述特征点云。该多线性模型实现了降维、高效计算，并在无需任何训练数据或额外信息的情况下提取数据模式及其几何结构。在严重欠采样条件下的dMRI数据数值测试表明，所提方法相较于其前代方法、主流数据建模方法以及近期基于张量和深度图像先验的方案，在效率和精度上均实现了显著提升。