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A compressed sensing approach to interpolation of fractional Brownian trajectories for a single particle tracking experiment

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  • Muszkieta, Monika
  • Janczura, Joanna

Abstract

In this paper, assuming that particles undergo the fractional Brownian motion, we propose the interpolation model based on the fact that the spectral density derived for the finite-length realization of this process obeys a power law decay. This allows us to apply the main idea of compressed sensing to reconstruct a given trajectory in the frequency domain. We conduct a simulation study with various trajectory degradation models reflecting typical limitations found in a single particle tracking experiment. Based on the statistical analysis we show that parameters characterizing the fractional Brownian motion estimated from trajectories interpolated by the proposed method are close to the ones estimated from the ground truth data.

Suggested Citation

  • Muszkieta, Monika & Janczura, Joanna, 2023. "A compressed sensing approach to interpolation of fractional Brownian trajectories for a single particle tracking experiment," Applied Mathematics and Computation, Elsevier, vol. 446(C).
    • Handle: RePEc:eee:apmaco:v:446:y:2023:i:c:s0096300323000693
    DOI: 10.1016/j.amc.2023.127900
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    References listed on IDEAS

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    1. Eldad Kepten & Aleksander Weron & Grzegorz Sikora & Krzysztof Burnecki & Yuval Garini, 2015. "Guidelines for the Fitting of Anomalous Diffusion Mean Square Displacement Graphs from Single Particle Tracking Experiments," PLOS ONE, Public Library of Science, vol. 10(2), pages 1-10, February.
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    3. Martin Lysy & Natesh S. Pillai & David B. Hill & M. Gregory Forest & John W. R. Mellnik & Paula A. Vasquez & Scott A. McKinley, 2016. "Model Comparison and Assessment for Single Particle Tracking in Biological Fluids," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(516), pages 1413-1426, October.
    4. Muszkieta, Monika & Janczura, Joanna & Weron, Aleksander, 2021. "Simulation and tracking of fractional particles motion. From microscopy video to statistical analysis. A Brownian bridge approach," Applied Mathematics and Computation, Elsevier, vol. 396(C).
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