Accelerated NMR Spectroscopy by Using Compressed Sensing
Accelerated NMR Spectroscopy by Using Compressed Sensing
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DOI：
10.1002/anie.201100370
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发表时间：
2011-01-01
影响因子：
16.6
通讯作者：
Orekhov, Vladislav Yu.
中科院分区：
文献类型：
--
作者：
Kazimierczuk, Krzysztof;Orekhov, Vladislav Yu.
在研究分子结构、相互作用和动力学方面，人们对高分辨率、快速的多维核磁共振波谱越来越感兴趣。当代核磁共振光谱学的显著特征，即可以同时观测复杂大分子中的数百个原子，其基础是20世纪70年代中期发明的多维实验。然而，这些实验获得的最终分辨率是以系统地对大型多维数据集进行采样所需的长数据收集时间为代价的。测量数据点的数量随着期望的光谱分辨率和多个维度的指数增加而呈多项式增加。[2]长时间采样的问题经常影响甚至阻碍多维光谱学在化学和分子生物学中的许多应用。幸运的是，快速核磁共振波谱领域提供了许多解决方案。[3-9]一种常见的方法是用随机非均匀采样(NUS)代替在精细奈奎斯特网格上对信号进行耗时的系统采样。然而，多年来，NUS与固有的光谱质量损失有关，例如光谱伪影和假峰的存在。最近，Cand S等人[10]提出了一个新的NUS定理，该定理指出，对于大多数实际情况，与完整Nyquist网格的大小相比，数据点的数量明显较少，就足以获得准确的谱重建。该定理引发了一组迅速增长的信号处理方法，称为压缩感知(CS)或压缩采样。最近在科学和技术的各个领域展示了CS的一些应用，包括在快速磁共振成像(MRI)中获得的显著结果。[11]在这里，我们展示了CS是从NUS数据中获得高质量光谱的有效工具，并给出了第一个压缩传感在核磁共振波谱(CS-NMR)中的实验例子。根据经典的Nyquist-Shannon采样定理，以等于或大于频谱带宽的恒定速率采样是精确重建频谱的必要条件。这个定理基于一个隐含的悲观假设，即频谱中的每个点都承载着重要的信息。然而，在大多数实际情况下，包括核磁共振光谱，峰只占光谱的一小部分，而其余的是基线。换句话说，我们说光谱是稀疏的。
There is increased interest in high-resolution, fast multidimensional NMR spectroscopy for studying molecular structure, interactions, and dynamics. The distinct feature of the contemporary NMR spectroscopy, namely the possibility to observe hundreds of atoms in complex macromolecules simultaneously, finds its foundation in the invention of multidimensional experiments in the mid 1970s.[1] However, the ultimate resolution obtained in these experiments comes at the high price of the long data collection times needed to systematically sample the large multidimensional data sets. The number of measured data points increases polynomialy with desired spectral resolution and exponentially with a number of dimensions.[2] The problem of lengthy sampling often compromises or even prohibits many applications of the multidimensional spectroscopy in chemistry and molecular biology. Fortunately, the field of fast NMR spectroscopy offers a number of solutions.[3–9] A common approach is to replace the time-consuming systematic sampling of the signal on the fine Nyquist grid by the random non-uniform sampling (NUS).[4] For many years, however, NUS was associated with the inherent loss of the spectrum quality, such as the presence of spectral artefacts and false peaks. Recently, Cand s et al.[10] formulated a new NUS theorem, which states that for most of the practical cases, a significantly smaller number of data points in comparison to the size the full Nyquist grid is sufficient for obtaining the exact reconstruction of the spectrum. The theorem evoked the rapidly growing group of signal processing methods, referred to as the compressed sensing (CS) or compressive sampling. A number of CS applications has been recently demonstrated in various fields of science and technology, including the striking results obtained for fast magnetic resonance imaging (MRI).[11] Herein, we demonstrate CS as an effective tool for obtaining high-quality spectra from the NUS data and present the first experimental examples of compressed sensing in NMR spectroscopy (CS-NMR). According to the classical Nyquist–Shannon sampling theorem, sampling at the constant rate, which is equal or larger than the spectral bandwidth, is the necessary condition for the exact reconstruction of the spectrum. This theorem is based on an implicit pessimistic assumption that every point in the spectrum carries important information. However, in the most of the practical cases, including the NMR spectroscopy, the peaks occupy only a small fraction of the spectrum, while the rest is the baseline. In other words, we say that the spectrum is sparse.