Details
| Original language | English |
|---|---|
| Pages (from-to) | 836-844 |
| Number of pages | 9 |
| Journal | Magnetic resonance in chemistry |
| Volume | 57 |
| Issue number | 10 |
| Early online date | 22 Jan 2019 |
| Publication status | Published - 14 Oct 2019 |
| Externally published | Yes |
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.
Keywords
- Laplace inversion, NMR relaxation, regularization
ASJC Scopus subject areas
- Chemistry(all)
- General Chemistry
- Materials Science(all)
- General Materials Science
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In: Magnetic resonance in chemistry, Vol. 57, No. 10, 14.10.2019, p. 836-844.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Regularized inversion of the Laplace transform for series of experiments
AU - Radel, B.
AU - Hardy, E.H.
AU - Djuric, Z.
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.
PY - 2019/10/14
Y1 - 2019/10/14
N2 - 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.
AB - 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.
KW - Laplace inversion
KW - NMR relaxation
KW - regularization
UR - http://www.scopus.com/inward/record.url?scp=85073522937&partnerID=8YFLogxK
U2 - 10.1002/mrc.4836
DO - 10.1002/mrc.4836
M3 - Article
VL - 57
SP - 836
EP - 844
JO - Magnetic resonance in chemistry
JF - Magnetic resonance in chemistry
SN - 0749-1581
IS - 10
ER -