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Iterative thresholding algorithm for multiexponential decay applied to PGSE NMR data.

Mateusz Urbańczyk1, Diana Bernin, Wiktor Koźmiński

  • 1Faculty of Chemistry, University of Warsaw, Pasteura 1, 02-093 Warsaw, Poland.

Analytical Chemistry
|January 10, 2013
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Summary

A new Iterative Thresholding Algorithm for Multiexponential Decay (ITAMeD) improves NMR diffusion coefficient analysis. This method enhances resolution for discrete diffusion coefficient distributions in monodispersed samples.

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Area of Science:

  • Nuclear Magnetic Resonance (NMR) Spectroscopy
  • Chemical Physics
  • Materials Science

Background:

  • Pulsed gradient spin echo (PGSE) is a standard NMR technique for measuring diffusion coefficients.
  • Analyzing multiexponential decays with an unknown number of components presents significant challenges in signal processing.

Purpose of the Study:

  • To introduce a novel signal processing method for analyzing challenging multiexponential NMR decays.
  • To improve the resolution and accuracy of diffusion coefficient determination in complex systems.

Main Methods:

  • Modification of Tikhonov's regularization using an l(1)-norm penalty function to enforce sparsity.
  • Implementation of the Iterative Thresholding Algorithm for Multiexponential Decay (ITAMeD) utilizing the Fast Iterative Shrinkage Thresholding Algorithm (FISTA).
  • Comparison of ITAMeD against established methods like CONTIN, Maximum Entropy (MaxEnt), Levenberg-Marquardt-Fletcher fitting, and Non-negative Least Squares (NNLS).

Main Results:

  • The l(1)-norm penalty function enforces sparsity, leading to improved resolution compared to CONTIN and MaxEnt.
  • ITAMeD demonstrated comparable or superior performance in noise vulnerability and resolution on simulated datasets.
  • Experimental validation on polyethylene glycol (PEG) solutions showed promising results, particularly for monodispersed samples.

Conclusions:

  • ITAMeD offers enhanced resolution and robustness for analyzing diffusion coefficients from multiexponential NMR signals.
  • The method is particularly suitable for samples with discrete distributions of diffusion coefficients.
  • ITAMeD represents a valuable advancement in NMR signal processing for materials characterization.