Lorentzian peak sharpening and sparse blind source separation for NMR spectroscopy
Lorentzian peak sharpening and sparse blind source separation for NMR spectroscopy
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DOI：
10.1007/s11760-021-02002-4
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发表时间：
2020-09
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通讯作者：
Yuanchang Sun;J. Xin
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文献类型：
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作者：
Yuanchang Sun;J. Xin
在本文中，我们介绍了一种用于非负数据和重叠数据的盲源分离的预处理技术。对于核磁共振波谱（NMR），Naanaa 和 Nuzillard（NN）的经典方法要求源信号在某些位置不重叠，而在其他地方允许它们相互重叠。 NN 的方法适用于具有独立峰 (SAP) 的数据信号。然而，SAP 并不完全适用于实际的 NMR 谱。违反 SAP 通常会在 NN 的分离结果中引入错误或伪影。为了解决这个问题，这里开发了一种基于洛伦兹峰形状和加权峰锐化的预处理技术。这个想法是将原始峰值信号与其加权负二阶导数叠加。由此产生的尖锐（更窄和更高）的峰值使 NN 的方法能够在更宽松的 SAP 条件（即所谓的主峰条件）下工作，并提供改进的结果。为了在保持数据非负性的同时实现最佳锐化，我们证明了权重参数上限的存在并提出了选择标准。核磁共振波谱数据的数值实验表明我们提出的方法具有令人满意的性能。
In this paper, we introduce a preprocessing technique for blind source separation of nonnegative and overlapped data. For nuclear magnetic resonance spectroscopy (NMR), the classical method of Naanaa and Nuzillard (NN) requires the condition that source signals to be non-overlapping at certain locations, while they are allowed to overlap with each other elsewhere. NN’s method works well with data signals that possess stand-alone peaks (SAPs). The SAP does not hold completely for realistic NMR spectra, however. Violation of SAP often introduces errors or artifacts in the NN’s separation results. To address this issue, a preprocessing technique is developed here based on Lorentzian peak shapes and weighted peak sharpening. The idea is to superimpose the original peak signal with its weighted negative second-order derivative. The resulting sharpened (narrower and taller) peaks enable NN’s method to work with a more relaxed SAP condition, the so-called dominant peaks condition, and deliver improved results. To achieve an optimal sharpening while preserving the data nonnegativity, we prove the existence of an upper bound of the weight parameter and propose a selection criterion. Numerical experiments on NMR spectroscopy data show satisfactory performance of our proposed method.