Non uniform sampling

Non uniform sampling (NUS) is a method for collecting a subset of the indirect points typically acquired, thereby reducing experiment time. As little as 10% of an indirect dimension can be collected without reducing spectral quality. NUS offers significant time savings, particularly for higher dimensionality experiments.

The panels below represent 2D data collection, traditional on the left and NUS on the right. Each horizontal red line represents a slice of the experiment that is collected. In traditional data collection, slices are collected in sequence, linearly sampling the chemical shift evolution in the t₁ dimension. With NUS, only a fraction of the points are collected (1/8 in this case) and the slices need not be collected in order. Randomising the slice collection order allows the experiment to be stopped early without truncating the signal decay. The best method for selecting which slices to collect is still the subject of some research¹ but pseudo-random spacing in which the gaps increase towards the end of the decay² , as shown here, works quite well. Obviously, NUS greatly reduces data collection time.



Of course, nothing comes for free, so the cost of reducing acquisition time is an increase in processing complexity and time. If the slices were collected in a random order they must first be placed in the correct order. Next, the missing slices are filled with zeroes. The panels below show a column from a 2D TOCSY experiment taken at δ_H 7.8 ppm after fourier transformation in the directly detected dimension. The left panel shows the interferogram from the fully sampled experiment and the right shows the interferogram from the NUS experiment after reordering of the data and replacement of the missing points with zeroes.


After reordering the NUS data, the points that were collected are used to predict the points that were skipped, similar to linear prediction. There are several algorithms available for reconstructing the missing data^3,4,5. Following reconstruction of the missing data, processing continues in the normal fashion with apodization, zero-filling and fourier transformation. The result is a spectrum with very little difference from one acquired with traditional sampling. Below are a pair of TOCSY experiments acquired on the same sample. The spectrum on the left was acquired with traditional sampling taking 98 minutes. The spectrum on the right was acquired using NUS and took 12 minutes.


The version of TopSpin on the Facility spectrometers is not capable of processing NUS data, however, newer versions can. Other software, such as NMRPipe, NMRFx and MNova can also handle NUS data. NUS pulse sequences for most of the standard experiments are available at the Skaggs NMR Facility. Come and talk to us if you want to try them out.

References
1. Mehdi Mobli and Jeffrey C. Hoch
"Nonuniform sampling and non-Fourier signal processing methods in multidimensional NMR."
Prog Nucl Magn Reson Spectrosc. 2014 Nov;83:21-41

2. Sven G. Hyberts, Koh Takeuchi and Gerhard Wagner
"Poisson-gap sampling and forward maximum entropy reconstruction for enhancing the resolution and sensitivity of protein NMR data."
J Am Chem Soc. 2010 Feb 24;132(7):2145-7

3. Victor Jaravine, Ilgis Ibraghimov and Vladislav Y. Orekhov
"Removal of a time barrier for high-resolution multidimensional NMR spectroscopy."
Nat Methods. 2006 Aug;3(8):605-7

4. Krzysztof Kazimierczuk and Vladislav Y. Orekhov
"Accelerated NMR Spectroscopy by Using Compressed Sensing."
Angew Chem Int Ed Engl. 2011 Jun 6;50(24):5556-9

5. Sven G. Hyberts, Alexander G. Milbradt, Andreas B. Wagner, Haribabu Arthanari and Gerhard Wagner
"Application of iterative soft thresholding for fast reconstruction of NMR data non-uniformly sampled with multidimensional Poisson Gap scheduling."
J Biomol NMR. 2012 Apr;52(4):315-27