Interpolating and extrapolating with hmsIST: seeking a tmax for optimal sensitivity, resolution and frequency accuracy

Abstract

Non-Uniform Sampling (NUS) has the potential to exploit the optimal resolution of high-field NMR instruments. This is not possible in 3D and 4D NMR experiments when using traditional uniform sampling due to the long overall measurement time. Nominally, uniformly sampled (US) time domain data acquired to a maximum evolution time tmax can be extended to high resolution via a virtual maximum evolution time t*max while extrapolating with linear prediction or iterative soft thresholding (IST). At the high resolution obtainable with extrapolation of US data, however, the accuracy of peak positions is compromised as observed when comparing inter- and intra-residue peaks in a 3D HNCA experiment. However, the accuracy of peak positions is largely improved by spreading the same number of acquired time domain data points non-uniformly over a larger evolution time to an optimal tmax followed by extrapolation to a total t*max and processing the data with an appropriate reconstruction method, such as hmsIST. To explore the optimum value of experimentally measured tmax to be reached non-uniformly with a given number of sampling points we have created test situations of time-equivalent experiments and evaluate sensitivity and accuracy of peak positions. Here we use signal-to-maximum-noise ratio as the decisive measure of sensitivity. We find that both sensitivity and resolution are optimal when PoissonGap sampling to a tmax of about ½*T2*. Digital resolution is further enhanced by extrapolating the range of acquired time domain data to 2*T2* but without measuring experimental points beyond ½*T2*.

Enhancing Compression Level for More Efficient Compressed Sensing and Other Lessons from NMR Spectroscopy

“…Thus, there is certain balance between the two effects. This fact is also connected to the observation that CS works more efficiently for the interpolation of the data rather than extrapolation [78].…”

Characterizing Protein Hydration Dynamics Using Solution NMR Spectroscopy

“…Non-uniform sampling takes advantage of the fact that only a small subset of the frequencies sampled contains signal information whereas the rest contain noise (Donoho, 2006). While the DFT can’t be directly applied to non-uniformly sampled data numerous reconstruction algorithms have been employed that can accurately reproduce the S/N and frequency information of NMR signals (Hyberts, Arthanari, & Wagner, 2012; Hyberts, Robson, & Wagner, 2013; Hyberts, Robson, & Wagner, 2017) (see also the Chapter by Robson and coworkers in these Volumes). NUS has been established for many three-dimensional and four-dimensional experiments.…”

Compressed sensing: Reconstruction of non‐uniformly sampled multidimensional NMR data

“…39 Nevertheless even using NUS approaches, triple resonance 3D backbone experiments are still typically recorded with modest spectral resolution due to time constraints. Recently a detailed comparison 63 was made to investigate different approaches for extending resolution in multidimensional experiments focussing on linear prediction or IST-based 53 extrapolation of uniformly sampled data vs IST reconstruction of NUS data sampling out to high resolution, combined with further IST based extrapolation (up to maximum 4*T 2 ), demonstrating the benefits of combined CS-based interpolation and extrapolation. The authors suggest that optimum sensitivity, resolution, and frequency reconstruction are achieved by acquiring data to 0.5*T 2 with further improvements to linewidth by extrapolating to 2*T 2 .…”