Non Uniform Sampling (NUS) NMR Processing

Background

In the last few years, Non-Uniform Sampling (NUS) has emerged as a very powerful tool to significantly speed up the acquisition of multidimensional NMR experiments due to the fact that only a subset of the usual linearly sampled data in the Nyquist grid is measured. 

Unfortunately, this fast acquisition modality introduces a new challenge as the normal Fourier Transform will fail and consequently, special processing techniques are required.

A number of sophisticated methods have been proposed for reconstructing sparsely sampled 2D and higher dimensionality NMR data, including Maximum Entropy, CLEAN, multidimensional decomposition method (MDD), Forward Maximum entropy (FM) and its fast version (FFM), SIFT and IST [1]. Most of these procedures are computationally very expensive and usually require the adjustment of some parameters.

NUS processing and Mnova 9.0: M.I.S.T

It has been the objective of Mestrelab to implement within Mnova 9.0 a new 2D NUS processing module that fulfills the following criteria:

• It must be computationally very fast whilst reconstructing the data reliably. 
• It should work fully automatically without user intervention. A minimum set of adjustable parameters might be used for special cases
• It should be compatible with any 2D acquisition protocol and with NMR instrument. 
• All these requirements have been met with the development of M.I.S.T, a Modified Iterative Soft Thresholding algorithm 

Proof of Concept: 1D NUS Processing:

Initial development of the MIST algorithm was done using synthetic, noise-free 1D-FIDs in which a number of points have been randomly set to zero using a Poisson gap sampling method. After having optimized the algorithm under these conditions, the same procedure was carried out using experimental 1D spectra. 

Figure 1 shows the results obtained with the 1H NMR spectrum of Ondansetron in which 75% of samples have been set to zero using a random Poisson gap sampling method. Regular FFT of this spectrum shows a spectrum heavily corrupted with noise. Finally, reconstruction of the FID using the MIST algorithm shows a spectrum that resembles the ideal FT spectrum very closely. 

Figure 1: (a) Standard, regularly sampled 1H NMR spectrum of Ondansetron. (b) FFT spectrum of the same experimental FID where 75% of the original data points have been set to zero using a random Poisson gap sampling method. (c) Result of reconstructing previously ‘corrupted’ FID using the MIST algorithm

Next step in our work consisted in extending the 1D MIST algorithm to operate with 2D spectra. 

MIST in action: 2D NUS Processing:

The performance of the algorithm is demonstrated with the HSQC spectrum shown in Figure 2. On the left, the uniformly sampled spectrum acquired with 96 complex increments in the indirect t1 dimension is shown. On the right, the NUS spectrum acquired with 48 complex increments randomly sampled (50% NUS). 

Figure 2: (a) Linearly sampled HSQC spectrum (96 complex increments) (b) MIST reconstruction of a NUS spectrum acquired with 48 complex increments randomly sampled. The two figures are shown using the same contour levels

Processing of the NUS spectrum was done fully automatically (just drag & drop into Mnova) and total processing time was less than 4 seconds (in my 4 core computer).

Supported NMR experiments

Presently, NUS algorithm implemented in Mnova 9.0 supports HSQC and HMBC experiments, both magnitude and phase sensitive. We have also found good results with COSY spectra. We have also tried it successfully with some NOESY/ROESY experiments, although we have to warn that with a few of them the performance has not been so good.  

CONCLUSIONS

Mnova 9.0 supports now NUS 2D spectra acquired in Bruker or Agilent instruments (more vendors will be included shortly).

Processing of these spectra is done via the new MIST algorithm. It has been shown that this algorithm is very fast, robust and can be executed in a fully unattended way. Furthermore, our method is not sensitive to phase distortions.

Note: Mnova 9 will be available in Mestrelab Web site (www.mestrelab.com) very soon. Meantime, this version can be downloaded it directly from HERE (Windows only for now). This link will only work for a few days though. 

Acknowledgments:

I thank Frank Delaglio, David Russell, Paul J Bowyer and Manolo Martin for kindly providing 2D NUS spectra

[1] S. G. Hyberts et al., “Application of iterative Soft thresholding for fast reconstruction of NMR data non-uniformly sampled with  multidimensional Poisson Gap  scheduling”, J. Biomol. NMR 52, 315–327 (2012) and references therein