Kernel Regression Imputation in Manifolds via Bi-Linear Modeling: The Dynamic-MRI Case

• DOI: 10.36227/techrxiv.14813673.v1
• Publication Date: 2021-06-21T16:41:54Z
• Authors: Konstantinos Slav...; Gaurav Shetty; Loris Cannelli; Gesualdo Scutari; Ukash Nakarmi; Leslie Ying
• Keywords: Imputation (statistics); Kernel (algebra)

This paper introduces a non-parametric kernel-based modeling framework for imputation by regression on data that are assumed to lie close an unknown-to-the-user smooth manifold in Euclidean space. The proposed framework, coined kernel manifolds (KRIM), needs no training operate. Aiming at computationally efficient solutions, KRIM utilizes small number of ``landmark'' data-points extract geometric information from the measured via parsimonious affine combinations (``linear patches''), which mimic concept tangent spaces and take place functional approximation spaces, namely reproducing Hilbert (RKHSs). Multiple complex RKHSs combined data-driven way surmount obstacle pin-pointing ``optimal'' parameters single through cross-validation. extracted is incorporated into design novel bi-linear data-approximation model, imputation-by-regression task takes form inverse problem solved iterative algorithm with guaranteed convergence stationary point non-convex loss function. To showcase modular character wide applicability KRIM, this highlights application dynamic magnetic resonance imaging (dMRI), where reconstruction high-resolution images severely under-sampled dMRI desired. Extensive numerical tests synthetic real demonstrate superior performance over state-of-the-art approaches under several metrics computational footprint.<br>