Statistical Learning of NMR tensors
Session 22 held virtually via zoom on 16th February 2021 featured Dr. Deepansh Srivastava, postdoc in Prof. Philip Grandinetti's research group at Ohio State University, U.S.A. Dr. Srivastava gave a talk on "Statistical Learning of Nuclear Magnetic Resonance (NMR) tensors from 2D Isotropic/Anisotropic Correlation NMR Spectra". The video was recorded live during the presentation and serves as an educative lecture.
Follow Dr. Srivastava:
Website: https://deepanshs.github.io/home/
Google scholar: https://scholar.google.com/citations?...
Short abstract: The talk features a direct inversion of 2D isotropic/anisotropic correlation ss-NMR spectra to 3D NMR tensor parameter distribution. The problem, regularized with TSVD and smooth-LASSO methods, promote stability, sparsity, and smoothness in the solution. An application of this method on spectra of non-crystalline material will be shown.
Abstract: Many linear inversion problems involving Fredholm integrals of the first kind are frequently encountered in the field of magnetic resonance. One important application is the direct inversion of a solid-state NMR spectrum containing multiple overlapping anisotropic sub-spectra to obtain a distribution of the tensor parameters. Because of the ill-conditioned nature of this inverse problem, we investigate the use of the truncated singular value decomposition (TSVD) and smooth least absolute shrinkage and selection operator (S-LASSO) based regularization method, which (a) stabilizes the solution and (b) promotes sparsity and smoothness in the solution. We also propose an unambiguous representation for the anisotropy parameters using a piecewise polar coordinate system to minimize rank deficiency in the inversion kernel. To obtain the optimum tensor parameter distribution, we implement the k-fold cross-validation, a statistical learning method, to determine the hyperparameters of the regularized inverse problem. In this talk, I'll show the details of the linear-inversion method along with numerous illustrative applications on purely anisotropic NMR spectra, both synthetic as well as experimental two-dimensional spectra correlating the isotropic and anisotropic frequencies.