Department of Chemistry, Massachusetts Institute of Technology, Cambridge, MA 02139, USA.
J Magn Reson. 2012 Jan;214(1):296-301. doi: 10.1016/j.jmr.2011.12.002. Epub 2011 Dec 10.
We show that a simple, general, and easily reproducible method for generating non-uniform sampling (NUS) schedules preserves the benefits of random sampling, including inherently reduced sampling artifacts, while removing the pitfalls associated with choosing an arbitrary seed. Sampling schedules are generated from a discrete cumulative distribution function (CDF) that closely fits the continuous CDF of the desired probability density function. We compare random and deterministic sampling using a Gaussian probability density function applied to 2D HSQC spectra. Data are processed using the previously published method of Spectroscopy by Integration of Frequency and Time domain data (SIFT). NUS spectra from deterministic sampling schedules were found to be at least as good as those from random schedules at the SIFT critical sampling density, and significantly better at half that sampling density. The method can be applied to any probability density function and generalized to greater than two dimensions.
我们展示了一种简单、通用且易于重现的非均匀采样（NUS）方案生成方法，该方法保留了随机采样的优势，包括固有减少的采样伪影，同时消除了与选择任意种子相关的陷阱。采样方案是从离散累积分布函数（CDF）生成的，该函数与所需概率密度函数的连续 CDF 紧密拟合。我们使用高斯概率密度函数比较了二维 HSQC 光谱的随机和确定性采样。使用先前发布的通过频率和时域数据集成进行光谱学的方法（SIFT）处理数据。在 SIFT 关键采样密度下，确定性采样方案的 NUS 光谱至少与随机方案一样好，而在采样密度减半时则要好得多。该方法可应用于任何概率密度函数，并可推广到二维以上。
