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Clustered sparsity and Poisson-gap sampling.

Paweł Kasprzak1,2, Mateusz Urbańczyk1,3, Krzysztof Kazimierczuk4

  • 1Centre of New Technologies, University of Warsaw, Banacha 2C, 02-097, Warsaw, Poland.

Journal of Biomolecular NMR
|November 5, 2021
PubMed
Summary

Poisson-gap (PG) schedules improve multidimensional NMR experiments by leveraging "clustered sparsity" in spectra, outperforming standard methods. This explains PG

Keywords:
Blue-noise samplingClustered sparsityCompressed sensingIterative soft thresholdingNon-uniform samplingPoisson-gap sampling

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Area of Science:

  • Nuclear Magnetic Resonance (NMR) Spectroscopy
  • Computational Chemistry
  • Data Science

Background:

  • Non-uniform sampling (NUS) accelerates multidimensional NMR experiments.
  • Poisson-gap (PG) schedules are popular for NUS but lack theoretical CS explanation.
  • Existing Compressed Sensing (CS) theory suggests flat pseudo-random generators are optimal.

Purpose of the Study:

  • To theoretically explain the effectiveness of Poisson-gap (PG) schedules in NMR spectroscopy.
  • To reconcile the practical success of PG with CS theory.
  • To identify spectral features that favor PG schedules.

Main Methods:

  • Theoretical analysis of PG schedules within CS framework.
  • Simulations of NMR data acquisition and reconstruction.
  • Analysis of experimental NMR data from the Biological Magnetic Resonance Bank (BMRB).

Main Results:

  • Identified "clustered sparsity" as a key feature in NMR spectra.
  • Demonstrated that PG schedules are well-suited for spectra with clustered sparsity.
  • Showed that denser sampling at signal edges can be beneficial.

Conclusions:

  • Poisson-gap schedules are theoretically justified for NMR spectra exhibiting "clustered sparsity".
  • The success of PG is linked to the specific structure of NMR spectral data.
  • Understanding spectral features like clustered sparsity optimizes NUS strategy selection.