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General regularization framework for DEER spectroscopy.

Luis Fábregas Ibáñez1, Gunnar Jeschke1

  • 1ETH Zurich, Lab. Phys. Chem., Vladimir-Prelog Weg 2, 8093 Zurich, Switzerland.

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|January 28, 2019
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Summary

Modern regularization methods, including Bregman iterations, offer improved distance distribution analysis for double electron-electron resonance (DEER) data compared to standard Tikhonov regularization, especially at moderate signal-to-noise ratios.

Keywords:
Bregman iterationsDEERDistance distributionsEPRHuberInverse problemOptimizationPELDORRegularizationTikhonovTotal variation

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Area of Science:

  • Biophysics
  • Computational Chemistry
  • Data Analysis

Background:

  • Tikhonov regularization is the standard method for analyzing double electron-electron resonance (DEER) data to determine distance distributions.
  • More advanced regularization techniques have emerged in other scientific fields.

Purpose of the Study:

  • To evaluate alternative regularization methods, including total variation (TV) and Huber penalties with Bregman iterations, against Tikhonov regularization for DEER data analysis.
  • To provide a general mathematical framework and open-source software for these methods.

Main Methods:

  • Analysis of Tikhonov, total variation (TV), and Huber penalties, with and without Bregman iterations.
  • Extension of regularization parameter selection methods.
  • Assessment using a large dataset of noisy DEER traces with known ground truth.

Main Results:

  • Bregman-iterative regularization methods show improvement over Tikhonov regularization.
  • These methods enhance feature recognition and distribution width recovery at moderate signal-to-noise ratios when noise variance is known.
  • Bregman-iterative methods demonstrate robustness in regularization parameter selection.

Conclusions:

  • Alternative regularization techniques, particularly those employing Bregman iterations, offer superior performance for DEER data processing compared to traditional Tikhonov regularization.
  • The developed framework and software facilitate the adoption of these advanced methods for more accurate distance distribution analysis.