Commonly used linear sampling of indirect dimensions in 3D and 4D NMR spectra cannot proceed to maximum evolution times needed to match natural line widths. This can only be achieved with non-uniform sampling (NUS). With the availability of high-fidelity reconstruction methods we can now routinely record and reconstruct 4D NUS spectra with less than 1% of the indirect points sampling up to 120 ms evolution times, within six days of measuring time. Recording this experiment linearly would take 500 days. Thus, NUS is needed to exploit the power of modern NMR instruments.
NUS can also increase the capability of detecting weak signals, such as in 3D or 4D NOESYs. Here we compare time-equivalent US and NUS experiments. If we record only 1% of the indirect points we can collect 100 times more scans per increment in the same amount of time. This increases both, the SNR and the probability of detecting weak peaks. This can be shown in simulations and experimentally1 .
To utilize these benefits it is important to apply optimal sampling schedules that focus on time-domain regions where the signal is strongest, to avoid large gaps, and to maximize randomness. We achieve this by selecting sampling gaps randomly according to a Poisson distribution centered at zero2 .
Finally, we need a high-fidelity reconstruction method. After working with and developing new reconstruction methods we have come up with a reliable and very fast approach based on the Iterative Soft Thresholding principle, hmsIST. It doesn’t create significant artifacts, yields correct peak heights and is very fast so that high-resolution 4D spectra can be recorded and reconstructed routinely within a day3 .