Regularized inversion of the Laplace transform for series of experiments. (21st February 2019)

• Record Type: Journal Article
• Authors: Radel, Benjamin; Hardy, Edme H.; Djuric, Zorana; Mahlbacher, Markus; Haist, Michael; Müller, Harald S.
• Other Names: Silva Elipe Maria Victoria guestEditor.
• Is Part Of: Magnetic resonance in chemistry. Volume 57:Number 10(2019)
• Page Start: 836
• Page End: 844
• Publication Date: 2019-02-21
• Subjects: Laplace inversion -- NMR relaxation -- regularization; Nuclear magnetic resonance spectroscopy -- Periodicals; Chemistry, Organic -- Periodicals; Magnetic resonance -- Periodicals; 538.36
• DOI: 10.1002/mrc.4836
• Languages: English
• ISSNs: 0749-1581

Abstract

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. Abstract : 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. 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.