Simulation-Based Sensitivity Analysis of Regularization Parameters for Robust Reconstruction of Complex Material’s T1 − T21H LF-NMR Energy Relaxation Signals

  • Salvatore Campisi-Pinto
  • Ofer Levi
  • Diamanta Benson
  • Maysa Teixeira Resende
  • Michael Saunders
  • Charles Linder
  • Zeev WiesmanEmail author
Original Paper


We recently showed, in a simulation study using two artificial signals, that our PDCO (Primal Dual interior method for Convex Objectives) reconstruction algorithm can be efficiently used for the reconstruction of low-field proton nuclear magnetic resonance (1H LF-NMR) relaxation signals into T1 (spin–lattice) vs. T2 (spin–spin) time 2D graphs of a material’s composition. In the present study, for highly complex materials, we demonstrate the PDCO’s reconstruction efficacy for a much wider range of simulated signals with higher complexity and different signal-to-noise ratios (SNR) taken from actual reconstructed 1H LF-NMR spectroscopy signals of oleic acid and cattle manure. The optimal regularization parameters of the PDCO’s reconstructing algorithm were identified for this large range of simulated LF-NMR signals and noise values. These simulated compact graphical and numerical representations demonstrated 1H LF-NMR relaxation signals of complex materials can be accurately reconstructed into T1 − T2 time graphs of a material’s chemical and morphology. The present study further confirmed that an optimal single set of regulatory parameters for the data reconstruction algorithms could be used for different materials or different batches of the same material.



The funding has been received from Israeli Ministry of Science and Technology (Grant No. 17572).


  1. 1.
    Z. Wiesman, C. Linder, T.M. Resende, N. Ayalon, O. Levi, O.D. Bernardinelli, L.A. Colnago, C.I. Nascimento Mitre, R. Jackman, Energy Fuels 32, 5090–5102 (2018)CrossRefGoogle Scholar
  2. 2.
    M.T. Resende, S. Campisi-Pinto, C. Linder, Z. Wiesman, J. Am. Oil Chem. Soc. 98, 125–135 (2019)CrossRefGoogle Scholar
  3. 3.
    P. Berman, O. Levi, Y. Parmet, M. Saunders, Z. Wiesman, Concepts Magn. Reson. Part A 42(3), 72–88 (2013)CrossRefGoogle Scholar
  4. 4.
    B. Hills, S. Benamira, N. Marigheto, K.T. Wright, Appl. Magn. Reson. 26(4), 543–560 (2004)CrossRefGoogle Scholar
  5. 5.
    S.S. Chen, D.L. Donoho, M.A. Saunders, SIAM Rev. 43(1), 129–159 (2001)ADSMathSciNetCrossRefGoogle Scholar
  6. 6.
    D.L. Donoho, I.E.E.E. Trans, Inf. Theory 52(4), 1289–1306 (2006)CrossRefGoogle Scholar
  7. 7.
    S. Campisi-Pinto, O. Levi, D. Benson, M. Cohen, M.T. Resende, M. Saunders, C. Linder, Z. Wiesman, Appl. Magn. Reson. 49(10), 1129–1150 (2018)CrossRefGoogle Scholar
  8. 8.
    P. Berman, N. Meiri, C. Linder, Z. Wiesman, Fuel 177, 315–325 (2016)CrossRefGoogle Scholar
  9. 9.
    A. Berman, O. Leshem, O. Etziony, Y. Levi, M. Parmet, Z. Saunders, Wiesman. Biotechnol. Biofuels 6(1), 55 (2013)CrossRefGoogle Scholar
  10. 10.
    B. Blümich, F. Casanova, S. Appelt, Chem. Phys. Lett. 477(4–6), 231–240 (2009)ADSCrossRefGoogle Scholar
  11. 11.
    Y. Song, L. Venkataramanan, M. Hürlimann, M. Flaum, P. Frulla, C. Straley, J. Magn. Reson. 154(2), 261–268 (2002)ADSCrossRefGoogle Scholar
  12. 12.
    M.D. Hürlimann, L. Burcaw, Y.Q. Song, J. Colloid Interface Sci. 297, 303–311 (2006)ADSCrossRefGoogle Scholar
  13. 13.
    P. Wang, L. Venkataramanan, V. Jain, IEEE Trans. Comput. Imaging 3(2), 355–368 (2017)MathSciNetCrossRefGoogle Scholar
  14. 14.
    C.J. Willmott, K. Matsuura, Int. J. Geogr. Inf. Sci. 20, 89–102 (2006)CrossRefGoogle Scholar
  15. 15.
    C.J. Willmott, S.M. Robeson, K. Matsuura, Int. J. Climatol. 32, 2088–2094 (2012)CrossRefGoogle Scholar
  16. 16.
    G. Scarchilli, E. Gorgucci, V. Chandrasekar, IEEE Trans. Geosci. Remote Sens. 37(2), 1122–1127 (1999)ADSCrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2019

Authors and Affiliations

  • Salvatore Campisi-Pinto
    • 1
    • 2
  • Ofer Levi
    • 2
  • Diamanta Benson
    • 2
  • Maysa Teixeira Resende
    • 1
  • Michael Saunders
    • 3
  • Charles Linder
    • 1
  • Zeev Wiesman
    • 1
    Email author
  1. 1.Phyto-Lipid Biotechnology Laboratory, Department of Biotechnology Engineering, Faculty of Engineering SciencesBen-Gurion University of the NegevBeer-ShevaIsrael
  2. 2.Department of Mathematics and Computer Science Program of Industrial Engineering and ManagementThe Open UniversityRa’ananaIsrael
  3. 3.Department of Management Science and Engineering (MS&E)Stanford UniversityStanfordUSA

Personalised recommendations