Optimal parameters for anomalous diffusion exponent estimation from noisy data

Abstract

The most common way of estimating the anomalous diffusion exponent from single-particle trajectories consists in a linear fitting of the dependence of the time averaged mean square displacement on the lag time at the log-log scale. However, various measurement noises that are unavoidably present in experimental data, can strongly deteriorate the quality of this estimation procedure and bias the estimated exponent. To investigate the impact of noises and to improve the estimation quality, we compare three approaches for estimating the anomalous diffusion exponent and check their efficiency on fractional Brownian motion corrupted by Gaussian noise. We discuss how the parameters of this anomalous diffusion model and the parameters of the estimation techniques influence the estimated exponent. We show that the conventional linear fitting is the least optimal method for the analysis of noisy data.

References in corpus (6)

• In vivo anomalous diffusion and weak ergodicity breaking of lipid granules
• Quantitative analysis of single particle trajectories: mean maximal excursion method
• A Test for Determining a Subdiffusive Model in Ergodic Systems from Single Trajectories
• Bayesian Decision Tree for the Classification of the Mode of Motion in Single-Molecule Trajectories
• Time-averaged MSD of Brownian motion
• Optimal and sub-optimal quadratic forms for non-centered Gaussian processes

Cited by in corpus (7)

• Measurement of Anomalous Diffusion Using Recurrent Neural Networks
• Classification of particle trajectories in living cells: machine learning versus statistical testing hypothesis for fractional anomalous diffusion
• Classification, inference and segmentation of anomalous diffusion with recurrent neural networks
• Learning physical properties of anomalous random walks using graph neural networks
• Boosting the performance of anomalous diffusion classifiers with the proper choice of features
• Superstatistical modelling of protein diffusion dynamics in bacteria
• Recurrent neural network analysis of single trajectories switching between anomalous diffusion states