Skip to main content
Log in

Reaching the sparse-sampling limit for reconstructing a single peak in a 2D NMR spectrum using iterated maps

  • Article
  • Published:
Journal of Biomolecular NMR Aims and scope Submit manuscript

Abstract

Many of the ubiquitous experiments of biomolecular NMR, including \(R_2\), \(R_{1\rho }\), and CEST, involve acquiring repeated 2D spectra under slightly different conditions. Such experiments are amenable to acceleration using non-uniform sampling spectral reconstruction methods that take advantage of prior information. We previously developed one such technique, an iterated maps method (DiffMap) that we successfully applied to 2D NMR spectra, including \(R_2\) relaxation dispersion data. In that prior work, we took a top-down approach to reconstructing the 2D spectrum with a minimal number of sparse samples, reaching an undersampling fraction that appeared to leave some room for improvement. In this study, we develop an in-depth understanding of the action of the DiffMap algorithm, identifying the factors that cause reconstruction errors for different undersampling fractions. This improved understanding allows us to formulate a bottom-up approach to finding the lowest number of sparse samples required to accurately reconstruct individual spectral features with DiffMap. We also discuss the difficulty of extending this method to reconstructing many peaks at once, and suggest a way forward.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12

Similar content being viewed by others

Notes

  1. Note that we are not calculating this SNR by comparing signal amplitude of a peak to noise amplitude far from all peaks after reconstruction, because this is known to be misleading (see e.g. Hyberts et al. (2017)). Instead, we are considering the ratio of the reconstructed amplitude to the expected variation in that amplitude, which we estimate using the \(E_\text {SZ}\) model explained above.

References

Download references

Acknowledgements

We thank G. Manley for acquiring the IGPS data set. We thank D. Cui, G. Manley, and S. Elrington for helpful discussions. J.P. Loria acknowledges the support of the NSF through Grant No. MCB-1615415, and the NIH through Grant No. GM112781. R. Blum, J. Rovny, and S. Barrett acknowledge the support of the NSF through Grant No. DMR-1610313 and Grant No. DMR-1310274. R. Blum is an NSF fellow and this material is based upon work supported by the NSF GRFP under Grant No. DGE-1122492.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Sean E. Barrett.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations

Electronic supplementary material

Below is the link to the electronic supplementary material.

Electronic supplementary material 1 (PDF 1779 kb)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Blum, R.L., Rovny, J., Loria, J.P. et al. Reaching the sparse-sampling limit for reconstructing a single peak in a 2D NMR spectrum using iterated maps. J Biomol NMR 73, 545–560 (2019). https://doi.org/10.1007/s10858-019-00262-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10858-019-00262-4

Keywords

Navigation