Decoherence Principles and Algorithms for One-Dimensional Nonuniform Sampling Schedules for Multidimensional NMR

Nonuniform sampling (NUS) NMR is a potent method for enabling diverse multidimensional NMR spectroscopies, but it depends on the quality of the sampling schedule, particularly for one-dimensional NUS (i.e., for 2D-NMR) and for sparser sampling where noise-like artifacts (aka sampling noise) are commonly observed. Current NUS scheduling algorithms, while generally effective, can also allow flaws that lead to increased artifactual noise in spectral reconstructions. Computation or expert user curation can improve such schedules but are not easily reproduced at the spectrometer. This work builds on lessons that reducing patterns in NUS schedules can reduce artifacts and aid sparser NUS. It is proposed here that patterns in a sampling schedule be treated sequentially at local and global scales. First, a localized decoherence filter is presented that leverages the properties of the binary Thue-Morse (TM) sequence to remediate patterned subsequences in the schedule. Next, an approach to polishing the point-spread-function (PSF) by an iterative thresholding method was developed, where improving the PSF treats the schedule globally. These algorithms are implemented in a hands-free scheduler for one-dimensional NUS and tested with both iterative soft thresholding (IST) and iterative line shape (SMILE) reconstructions. While varying degrees of sampling noise are still expected, particularly in sparser NUS conditions, these methods reduce larger spectral artifacts and perform more consistent design of schedules for broader use, as illustrated with sodium naproxen, strychnine, and u-¹³C,¹⁵N-ubiquitin for weighted (e.g., quantile, Poisson gap, exponential), and random unweighted (RU) NUS, though limitations of sparse RU-NUS should be considered.