Centre for Advanced Imaging, The University of Queensland, St. Lucia, QLD 4072, Australia.
Centre for Advanced Imaging, The University of Queensland, St. Lucia, QLD 4072, Australia.
J Magn Reson. 2019 Mar;300:103-113. doi: 10.1016/j.jmr.2019.01.014. Epub 2019 Jan 26.
The grouping of data in bursts, also referred to as clusters, spikes or clumps, is a common phenomenon in stochastic sampling. There have been several reports that suggest that in NMR, the presence of such bursts is beneficial to spectral reconstruction where data are sampled nonuniformly. In this work, we seek to define a mode of sampling that produces bursts of randomly distributed data in a controlled manner. An algorithm is described for achieving this where the burst length and its uniformity is controlled - we refer to this type of sampling mode as clustered sampling. Measures are introduced for assessing the "burstiness" of nonuniformly sampled data in multiple dimensions and properties of the point-spread-function of these schedules are assessed. The clustered sampling method is applied to samples drawn from an exponentially weighted distribution either distributed randomly or pseudo-randomly by use of a jittering algorithm. The results reveal that bursts introduce characteristic sampling artifacts that are shifted to low frequencies (red shifted), with respect to the signal frequency, and that they produce artifact-reduced regions at frequencies related to the burst length. This observation is contrary to that observed for sampling methods that seek to evenly distribute NUS data, such as jittered or Poisson sampling. Extensive evaluation of simulated data with comparable inherent sensitivity, reveals that at high sampling coverage (25% in 1D), the distribution of the data has little impact on common spectral quality measures. Application of the introduced clustered sampling method to an experimental 3D NOESY experiment showed results consistent with that found for the simulated 1D data. However, in the extremes of very sparse sampling, the results suggest that there may be some advantages associated with incorporation of bursts in nonuniform sampling. The tools and theory presented will serve as a starting point to further explore this novel mode of sampling in NMR.
数据以突发（burst）的形式分组，也称为聚类（cluster）、尖峰（spike）或团块（clump），这是随机采样中的一种常见现象。有几项报告表明，在 NMR 中，存在这种突发对非均匀采样的数据的谱重建是有益的。在这项工作中，我们试图定义一种以受控方式产生随机分布数据突发的采样模式。描述了一种实现此目的的算法，其中控制突发长度及其均匀性 - 我们将这种采样模式称为聚类采样（clustered sampling）。引入了用于评估多维非均匀采样数据的“突发”程度的度量标准，并评估了这些方案的点扩散函数的性质。将聚类采样方法应用于从指数加权分布中提取的样本，这些样本要么是随机分布的，要么是通过抖动算法伪随机分布的。结果表明，突发会引入特征性的采样伪影，相对于信号频率向低频（红移）移动，并且它们在与突发长度相关的频率处产生伪影减少的区域。这一观察结果与旨在均匀分布 NUS 数据的采样方法（例如抖动或泊松采样）相反。对具有可比固有灵敏度的模拟数据的广泛评估表明，在高采样覆盖率（1D 中为 25%）下，数据的分布对常见的谱质量度量几乎没有影响。将引入的聚类采样方法应用于实验 3D NOESY 实验，结果与模拟 1D 数据的结果一致。然而，在非常稀疏采样的极端情况下，结果表明在非均匀采样中包含突发可能会带来一些优势。提出的工具和理论将作为进一步探索 NMR 中这种新型采样模式的起点。
