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Obtaining sparse distributions in 2D inverse problems.

A Reci1, A J Sederman1, L F Gladden1

  • 1Department of Chemical Engineering and Biotechnology, University of Cambridge, Pembroke Street, Cambridge CB2 3RA, United Kingdom.

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|June 18, 2017
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Summary
This summary is machine-generated.

L1 regularization offers superior performance for sparse inverse problems in NMR, accurately reconstructing system properties even with low signal-to-noise ratios. This method enhances resolution for analyzing complex mixtures in porous materials.

Keywords:
2D NMR correlation experiments2D inverse Laplace transformationInverse problemsL(1) regularization

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Area of Science:

  • Applied Mathematics and Spectroscopy
  • Nuclear Magnetic Resonance (NMR) Spectroscopy
  • Materials Science and Engineering

Background:

  • Inverse problems are crucial in science and engineering for estimating system properties.
  • Sparse inverse problems, where properties are not continuous, benefit from L1 regularization.
  • NMR correlation experiments (T1-T2, D-T2) are vital for characterizing porous materials and surface interactions.

Purpose of the Study:

  • To apply L1 regularization to NMR relaxation-relaxation (T1-T2) and diffusion-relaxation (D-T2) correlation experiments.
  • To develop and guide the implementation of a robust L1 regularization algorithm for these NMR applications.
  • To experimentally demonstrate the advantages of L1 regularization over Non-Negative Least Squares (NNLS) and Tikhonov regularization.

Main Methods:

  • Development of a robust algorithm for solving L1 regularization problems in NMR spectroscopy.
  • Experimental application of L1 regularization to T1-T2 and D-T2 correlation experiments.
  • Comparison of L1 regularization with NNLS and Tikhonov methods using signal-to-noise ratio and resolution metrics.

Main Results:

  • L1 regularization stably recovers distributions at signal-to-noise ratios below 20.
  • The method resolves relaxation time constants and diffusion coefficients differing by as little as 10%.
  • Successfully measured inter- and intra-particle concentrations of hexane and dodecane in porous silica, outperforming NNLS and Tikhonov.

Conclusions:

  • L1 regularization provides significant advantages over NNLS and Tikhonov for sparse inverse problems in NMR.
  • The enhanced resolving capability enables discrimination of chemical species and measurement of composition in porous media.
  • This approach offers stable and accurate analysis even in the presence of high noise levels.