Non-uniform sampling (NUS) is a popular way of reducing the amount of time taken by multidimensional NMR experiments. Among the various non-uniform sampling schemes that exist, the Poisson-gap (PG) schedules are particularly popular, especially when combined with compressed-sensing (CS) reconstruction of missing data points. However, the use of PG is based mainly on practical experience and has not, as yet, been explained in terms of CS theory. Moreover, an apparent contradiction exists between the reported effectiveness of PG and CS theory, which states that a “flat” pseudo-random generator is the best way to generate sampling schedules in order to reconstruct sparse spectra. In this paper we explain how, and in what situations, PG reveals its superior features in NMR spectroscopy. We support our theoretical considerations with simulations and analyses of experimental data from the Biological Magnetic Resonance Bank (BMRB). Our analyses reveal a previously unnoticed feature of many NMR spectra that explains the success of ”blue-noise” schedules, such as PG. We call this feature “clustered sparsity”. This refers to the fact that the peaks in NMR spectra are not just sparse but often form clusters in the indirect dimension, and PG is particularly suited to deal with such situations. Additionally, we discuss why denser sampling in the initial and final parts of the clustered signal may be useful.

非均匀采样 (NUS) 是一种减少多维 NMR 实验所用时间的流行方法。在现有的各种非均匀采样方案中，泊松间隙 (PG) 计划特别流行，尤其是在与缺失数据点的压缩感知 (CS) 重建相结合时。然而，PG 的使用主要是基于实践经验，目前还没有根据 CS 理论进行解释。此外，所报道的 PG 和 CS 理论的有效性之间存在明显的矛盾，该理论指出“扁平”伪随机发生器是生成采样计划以重建稀疏光谱的最佳方式。在本文中，我们解释了 PG 如何以及在什么情况下揭示其在 NMR 光谱中的优越特性。我们通过模拟和分析来自生物磁共振库 (BMRB) 的实验数据来支持我们的理论考虑。我们的分析揭示了许多 NMR 光谱以前未被注意到的特征，这解释了“蓝噪声”计划的成功，例如 PG。我们将此特征称为“集群稀疏性”。这是指核磁共振光谱中的峰不仅稀疏而且在间接维度上经常形成簇，而PG特别适合处理这种情况。此外，我们讨论了为什么在聚类信号的初始和最终部分进行更密集的采样可能是有用的。我们将此特征称为“集群稀疏性”。这是指核磁共振光谱中的峰不仅稀疏而且在间接维度上经常形成簇，而PG特别适合处理这种情况。此外，我们讨论了为什么在聚类信号的初始和最终部分进行更密集的采样可能是有用的。我们将此特征称为“集群稀疏性”。这是指核磁共振光谱中的峰不仅稀疏而且在间接维度上经常形成簇，而PG特别适合处理这种情况。此外，我们讨论了为什么在聚类信号的初始和最终部分进行更密集的采样可能是有用的。