Analysis of the Regularization Parameters of Primal–Dual Interior Method for Convex Objectives Applied to 1H Low Field Nuclear Magnetic Resonance Data Processing
- Authors: Campisi-Pinto S.1,2, Levi O.2, Benson D.2, Cohen M.1, Resende M.T.1, Saunders M.3, Linder C.1, Wiesman Z.1
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Affiliations:
- Phyto-Lipid Biotechnology Laboratory, Department of Biotechnology Engineering, Faculty of Engineering Sciences, Ben-Gurion University of the Negev
- Department of Mathematics and Computer Science Program of Industrial Engineering and Management, The Open University
- Department of Management Science and Engineering (MS&E), Stanford University
- Issue: Vol 49, No 10 (2018)
- Pages: 1129-1150
- Section: Original Paper
- URL: https://journals.rcsi.science/0937-9347/article/view/248191
- DOI: https://doi.org/10.1007/s00723-018-1048-4
- ID: 248191
Cite item
Abstract
Two-dimensional low-field hydrogen nuclear magnetic resonance (2D 1H LF-NMR) analysis of chemical compounds measures T1 and T2 relaxation times observed as exponential decay curves. Once relaxation curves are measured and stored in the format of discrete digital signals, they must be transformed, mathematically, into spectra that can be read and interpreted. We used primal–dual interior method for convex objectives (PDCO) that provided more accurate reconstructions than the standard algorithms. It is the objective of this paper to estimate the most suitable PDCO parameterization that provide accurate and robust reconstructions of relaxation curves into 2D spectra for LF-NMR under different signal-to-noise ratios. Finding optimal regularization parameters is an active field of mathematical research. PDCO, however, by making use of two regularization parameters instead of a single one, presents a much harder task, where the consolidated search criteria of a single parameter cannot be extended to two parameters. We featured a method based on numerical experiments and simulations that identified optimal and unique model coefficients that maximize PDCO reconstruction accuracy under different signal-to-noise conditions. The coefficients, as determined for artificial signals, increase the confidence of accurate reconstruction for 2D LF-NMR analysis on real lab samples.
About the authors
Salvatore Campisi-Pinto
Phyto-Lipid Biotechnology Laboratory, Department of Biotechnology Engineering, Faculty of Engineering Sciences, Ben-Gurion University of the Negev; Department of Mathematics and Computer Science Program of Industrial Engineering and Management, The Open University
Email: wiesman@bgu.ac.il
Israel, Beer-Sheva, 84105; Derekh ha-Universita 1, Ra’anana, 4353701
Ofer Levi
Department of Mathematics and Computer Science Program of Industrial Engineering and Management, The Open University
Email: wiesman@bgu.ac.il
Israel, Derekh ha-Universita 1, Ra’anana, 4353701
Diamanta Benson
Department of Mathematics and Computer Science Program of Industrial Engineering and Management, The Open University
Email: wiesman@bgu.ac.il
Israel, Derekh ha-Universita 1, Ra’anana, 4353701
Meir Cohen
Phyto-Lipid Biotechnology Laboratory, Department of Biotechnology Engineering, Faculty of Engineering Sciences, Ben-Gurion University of the Negev
Email: wiesman@bgu.ac.il
Israel, Beer-Sheva, 84105
Maysa Teixeira Resende
Phyto-Lipid Biotechnology Laboratory, Department of Biotechnology Engineering, Faculty of Engineering Sciences, Ben-Gurion University of the Negev
Email: wiesman@bgu.ac.il
Israel, Beer-Sheva, 84105
Michael Saunders
Department of Management Science and Engineering (MS&E), Stanford University
Email: wiesman@bgu.ac.il
United States, 475 Via Ortega, Stanford, CA, 94305-4042
Charles Linder
Phyto-Lipid Biotechnology Laboratory, Department of Biotechnology Engineering, Faculty of Engineering Sciences, Ben-Gurion University of the Negev
Email: wiesman@bgu.ac.il
Israel, Beer-Sheva, 84105
Zeev Wiesman
Phyto-Lipid Biotechnology Laboratory, Department of Biotechnology Engineering, Faculty of Engineering Sciences, Ben-Gurion University of the Negev
Author for correspondence.
Email: wiesman@bgu.ac.il
Israel, Beer-Sheva, 84105