Quantitative Comparisons of Single Particle Tracking Algorithms Quantitative Comparison of Single Particle Tracking Algorithms Across Different Signal and Noise Levels

Abstract

Single Particle Tracking (SPT) is a powerful class of tools for acquiring information about the dynamics of biological macromolecules moving inside living cells. In this work, we are interested in comparing algorithms with respect to the performance of localization and motion model estimation at very low signal levels. A standard approach for estimation is to use Gaussian Fitting (GF) to determine the position of an emitter in an image, followed by linking to produce a trajectory. These trajectories are then analyzed by using Mean Square Displacement (MSD) or Maximum Likelihood (ML) to estimate motion parameters, such as diffusion coefficients. However, both MSD and the standard formulation of ML assume a linear measurement model with simple additive Gaussian noise, which begins to fail as image intensity decreases. We have introduced two nonlinear methods that more accurately model camera-based measurements: Sequential Monte Carlo combined with Expectation Maximization (SMC-EM), and Unscented Kalman Filter combined with Expectation Maximization (U-EM). To compare the performance of SMC-EM and U-EM with the standard approach in localization and parameter estimation at low signal levels, we simulated SPT experiments of a single particle diffusing in two dimensions. Images were generated from a basic camera model together with shot noise. The results indicate that across different signal and noise level settings (especially with low signal levels), both SMC-EM and U-EM outperform GF-MSD and GF-MLE in localization and parameter estimation. It is important to note that U-EM is significantly cheaper in computation than SMC-EM. In future work, we would like to take into consideration time-varying motion models and other observation models with camera-specific noise.