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On the inversion of diffusion NMR data: Tikhonov regularization and optimal choice of the regularization parameter

journal contribution
posted on 2023-06-07, 20:00 authored by Iain Day
The analysis of diffusion NMR data in terms of distributions of diffusion coefficients is hampered by the ill-posed nature of the required inverse Laplace transformation. Nave approaches such as multiexponen- tial fitting or standard least-squares algorithms are numerically unstable and often fail. This paper updates the CONTIN approach of the application of Tikhonov regularization to stabilise this numerical inversion problem and demonstrates two methods for automatically choosing the optimal value of the regularization parameter. These approaches are computationally efficient and easy to implement using standard matrix algebra techniques. Example analyses are presenting using both synthetic data and experimental results of diffusion NMR studies on the azo-dye sunset yellow and some polymer molecular weight reference standards.

History

Publication status

  • Published

Journal

Journal of Magnetic Resonance

ISSN

1090-7807

Publisher

Elsevier

Issue

2

Volume

211

Page range

178-185

Department affiliated with

  • Chemistry Publications

Full text available

  • No

Peer reviewed?

  • Yes

Legacy Posted Date

2012-02-06

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