Journal of Biomolecular NMR

, Volume 62, Issue 1, pp 105–117 | Cite as

Efficient and generalized processing of multidimensional NUS NMR data: the NESTA algorithm and comparison of regularization terms

  • Shangjin Sun
  • Michelle Gill
  • Yifei Li
  • Mitchell Huang
  • R. Andrew Byrd


The advantages of non-uniform sampling (NUS) in offering time savings and resolution enhancement in NMR experiments have been increasingly recognized. The possibility of sensitivity gain by NUS has also been demonstrated. Application of NUS to multidimensional NMR experiments requires the selection of a sampling scheme and a reconstruction scheme to generate uniformly sampled time domain data. In this report, an efficient reconstruction scheme is presented and used to evaluate a range of regularization algorithms that collectively yield a generalized solution to processing NUS data in multidimensional NMR experiments. We compare l1-norm (L1), iterative re-weighted l1-norm (IRL1), and Gaussian smoothed l0-norm (Gaussian-SL0) regularization for processing multidimensional NUS NMR data. Based on the reconstruction of different multidimensional NUS NMR data sets, L1 is demonstrated to be a fast and accurate reconstruction method for both quantitative, high dynamic range applications (e.g. NOESY) and for all J-coupled correlation experiments. Compared to L1, both IRL1 and Gaussian-SL0 are shown to produce slightly higher quality reconstructions with improved linearity in peak intensities, albeit with a computational cost. Finally, a generalized processing system, NESTA-NMR, is described that utilizes a fast and accurate first-order gradient descent algorithm (NESTA) recently developed in the compressed sensing field. NESTA-NMR incorporates L1, IRL1, and Gaussian-SL0 regularization. NESTA-NMR is demonstrated to provide an efficient, streamlined approach to handling all types of multidimensional NMR data using proteins ranging in size from 8 to 32 kDa.


Non-uniform sampling Multidimensional NMR data processing Compressed sensing NESTA NUS gp78 ASAP1 



We thank Dr. Aleksandras Gutmanas (EBI, Hinxton, UK), Dr. Jinfa Ying (NIDDK, NIH, Bethesda, MD) and Mr. William Hanisch for useful discussions. This work was supported by the Intramural Research Program of the National Institutes of Health, National Cancer Institute, Center for Cancer Research.

Supplementary material

10858_2015_9923_MOESM1_ESM.pdf (1.2 mb)
Supplementary material 1 (PDF 1269 kb)


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Copyright information

© Springer Science+Business Media Dordrecht (outside the USA) 2015

Authors and Affiliations

  • Shangjin Sun
    • 1
  • Michelle Gill
    • 1
  • Yifei Li
    • 1
  • Mitchell Huang
    • 1
  • R. Andrew Byrd
    • 1
  1. 1.Structural Biophysics LaboratoryNational Cancer InstituteFrederickUSA

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