Statistics Seminar - Multi-linear kernel regression and imputation data manifolds: The dynamic-MRI case

Dates

Tuesday, May 2, 2023 - 11:00 to 12:00

Speaker: Konstantinos Slavakis (Tokyo Institute of Technology)

Abstract: This talk discusses a novel efficient multi-linear nonparametric (kernel-based) approximation framework for data regression and imputation, and its application to dynamic magnetic-resonance imaging (dMRI). The framework is built on the assumption that data features reside in or close to an unknown-to-the-user 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 proposed 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.