Institute of Mechanical Process Engineering and Mechanics, Karlsruhe Institute of Technology, Karlsruhe, Germany.
Institute of Concrete Structures and Building Materials, Karlsruhe Institute of Technology, Karlsruhe, Germany.
Magn Reson Chem. 2019 Aug;57(10):836-844. doi: 10.1002/mrc.4836. Epub 2019 Feb 21.
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.
不仅在低场核磁共振中，拉普拉斯反演也是一个相关且具有挑战性的话题。已经取得了相当大的概念和技术进展，特别是对于编码两个衰减维度的数据的反演。即使是适度的噪声也会导致过度拟合而使谱失真，这就需要先验平滑的谱。在本贡献中，我们处理简单快速的一维衰减实验的情况，这些实验在一个系列中被重复多次，以便研究样品或过程的演变。通过引入先验知识，即在序列维度上的演变也应该是平滑的，我们可以稳定峰位置并提高衰减维度的分辨率。解释了如何通过非常简单的方式扩展标准的一维正则化拉普拉斯反演，以便在序列维度上包含正则化。对于模拟数据和实验数据，都呈现了与一维序列反演相比的明显改进。对于后者，与多指数拟合进行了比较。
