Regularized inversion of the Laplace transform for series of experiments

Publikation: Beitrag in FachzeitschriftArtikelForschungPeer-Review

Autorschaft

  • B. Radel
  • E.H. Hardy
  • Z. Djuric
  • M. Mahlbacher
  • M. Haist
  • H.S. Müller

Externe Organisationen

  • Karlsruher Institut für Technologie (KIT)
Forschungs-netzwerk anzeigen

Details

OriginalspracheEnglisch
Seiten (von - bis)836-844
Seitenumfang9
FachzeitschriftMagnetic resonance in chemistry
Jahrgang57
Ausgabenummer10
Frühes Online-Datum22 Jan. 2019
PublikationsstatusVeröffentlicht - 14 Okt. 2019
Extern publiziertJa

Abstract

Not only in low-field nuclear magnetic resonance, Laplace inversion is a relevant and challenging topic. Considerable conceptual and technical progress has been made, especially for the inversion of data encoding two decay dimensions. Distortion of spectra by overfitting of even moderate noise is counteracted requiring a priori smooth spectra. In this contribution, we treat the case of simple and fast one-dimensional decay experiments that are repeated many times in a series in order to study the evolution of a sample or process. Incorporating the a priori knowledge that also in the series dimension evolution should be smooth, peak position can be stabilized and resolution improved in the decay dimension. It is explained how the standard one-dimensional regularized Laplace inversion can be extended quite simply in order to include regularization in the series dimension. Obvious improvements compared with series of one-dimensional inversions are presented for simulated as well as experimental data. For the latter, comparison with multiexponential fitting is performed.

ASJC Scopus Sachgebiete

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Regularized inversion of the Laplace transform for series of experiments. / Radel, B.; Hardy, E.H.; Djuric, Z. et al.
in: Magnetic resonance in chemistry, Jahrgang 57, Nr. 10, 14.10.2019, S. 836-844.

Publikation: Beitrag in FachzeitschriftArtikelForschungPeer-Review

Radel, B, Hardy, EH, Djuric, Z, Mahlbacher, M, Haist, M & Müller, HS 2019, 'Regularized inversion of the Laplace transform for series of experiments', Magnetic resonance in chemistry, Jg. 57, Nr. 10, S. 836-844. https://doi.org/10.1002/mrc.4836
Radel, B., Hardy, E. H., Djuric, Z., Mahlbacher, M., Haist, M., & Müller, H. S. (2019). Regularized inversion of the Laplace transform for series of experiments. Magnetic resonance in chemistry, 57(10), 836-844. https://doi.org/10.1002/mrc.4836
Radel B, Hardy EH, Djuric Z, Mahlbacher M, Haist M, Müller HS. Regularized inversion of the Laplace transform for series of experiments. Magnetic resonance in chemistry. 2019 Okt 14;57(10):836-844. Epub 2019 Jan 22. doi: 10.1002/mrc.4836
Radel, B. ; Hardy, E.H. ; Djuric, Z. et al. / Regularized inversion of the Laplace transform for series of experiments. in: Magnetic resonance in chemistry. 2019 ; Jahrgang 57, Nr. 10. S. 836-844.
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AU - Hardy, E.H.

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AU - Mahlbacher, M.

AU - Haist, M.

AU - Müller, H.S.

N1 - Funding Information: The authors thank the German Research Foundation forfunding the projects MU 1368/13-1 and HA 2840/6-1. G.Guthausen, Karlsruher Institut of Technology, G. Grossand K. Zick, Bruker Corporation, J. Sester, and V. Spinnlerare acknowledged for providing experimental data andhelpful discussion. Publisher Copyright: © 2019 John Wiley & Sons, Ltd.

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