数据流形中的多线性核回归与插补
Multi-Linear Kernel Regression and Imputation in Data Manifolds
AI总结：
本文提出一种用于数据回归与插补的高效多线性非参数近似框架，通过地标点和线性近似块在再生核 Hilbert 空间中建模流形几何，无需训练数据即可降维并提取模式，在动态磁共振成像实验中显著提升了效率与精度。
摘要：
本文引入了一种高效的多线性非参数（基于核的）近似框架，用于数据回归和插补，并将其应用于动态磁共振成像（dMRI）。假设数据特征驻留在嵌入在再生核 Hilbert 空间中的平滑流形上或附近。通过识别地标点，利用线性近似块来简洁地描述特征点云，这些近似块模仿了平滑流形切空间的概念。该多线性模型实现了降维，支持高效计算，并能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，与现有方法、流行的数据建模方法以及近期基于张量和深度图像先验的方案相比，所提方法在效率和准确性上均有显著提升。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
