Uncertainty quantification and estimation in differential dynamic microscopy

TL;DR

This paper introduces DDM-UQ, a new method that enhances differential dynamic microscopy by quantifying uncertainty, reducing computational cost, and improving robustness, enabling more routine and high-throughput analysis of dynamical systems.

Contribution

The authors develop a statistical framework for DDM that quantifies noise, reduces computational complexity, and employs Gaussian process regression for efficient analysis, which is novel in DDM.

Findings

DDM-UQ reduces computational cost by 95% using Gaussian process regression.

The method accurately estimates dynamical properties with validated simulations and experiments.

DDM-UQ improves robustness and noise quantification in DDM analysis.

Abstract

Differential dynamic microscopy (DDM) is a form of video image analysis that combines the sensitivity of scattering and the direct visualization benefits of microscopy. DDM is broadly useful in determining dynamical properties including the intermediate scattering function for many spatiotemporally correlated systems. Despite its straightforward analysis, DDM has not been fully adopted as a routine characterization tool, largely due to computational cost and lack of algorithmic robustness. We present statistical analysis that quantifies the noise, reduces the computational order and enhances the robustness of DDM analysis. We propagate the image noise through the Fourier analysis, which allows us to comprehensively study the bias in different estimators of model parameters, and we derive a different way to detect whether the bias is negligible. Furthermore, through use of Gaussian process regression (GPR), we find that predictive samples of the image structure function require only around 0.5%-5% of the Fourier transforms of the observed quantities. This vastly reduces computational cost, while preserving information of the quantities of interest, such as quantiles of the image scattering function, for subsequent analysis. The approach, which we call DDM with uncertainty quantification (DDM-UQ), is validated using both simulations and experiments with respect to accuracy and computational efficiency, as compared with conventional DDM and multiple particle tracking. Overall, we propose that DDM-UQ lays the foundation for important new applications of DDM, as well as to high-throughput characterization. We implement the fast computation tool in a new, publicly available MATLAB software package.