Single Particle Tracking (SPT) plays an important role in the study of physical and dynamic properties of biomolecules moving in their native environment. To date, many algorithms have been developed for localization and parameter estimation in SPT. Though the performance of these methods is good when the signal level is high and the motion model simple, they begin to fail as the signal level decreases or model complexity increases. In addition, the inputs to the SPT algorithms are sequences of images that are cropped from a large data set and that focus on a single particle. This motivates us to seek machine learning tools to deal with that initial step of extracting data from larger images containing multiple particles. This thesis makes contributions to both data extraction question and to the problem of state and parameter estimation.
First, we build upon the Expectation Maximization (EM) algorithm to create a generic framework for joint localization refinement and parameter estimation in SPT. Under the EM-based scheme, two representative methods are considered for generating the filtered and smoothed distributions needed by EM: Sequential Monte Carlo - Expectation Maximization (SMC-EM), and Unscented - Expectation Maximization (U-EM). The selection of filtering and smoothing algorithms is very flexible so long as they provide the necessary distributions for EM. The versatility and reliability of EM based framework have been validated via data-intensive modeling and simulation where we considered a variety of influential factors, such as a wide range of {\color{red}Signal-to-background ratios (SBRs)}, diffusion speeds, motion blur, camera types, image length, etc.
Meanwhile, under the EM-based scheme, we make an effort to improve the overall computational efficiency by simplifying the mathematical expression of models, replacing filtering/smoothing algorithms with more efficient ones {\color{purple} (trading some accuracy for reduced computation time)}, and using parallel computation and other computing techniques. In terms of localization refinement and parameter estimation in SPT, we also conduct an overall quantitative comparison among EM based methods and standard two-step methods. Regarding the U-EM, we conduct transformation methods to make it adapted to the nonlinearities and complexities of measurement model. We also extended the application of U-EM to more complicated SPT scenarios, including time-varying parameters and additional observation models that are relevant to the biophysical setting.
The second area of contribution is in the particle detection and extraction problem to create data to feed into the EM-based approaches. Here we build Particle Identification Networks (PINs) covering three different network architectures. The first, \PINCNN{}, is based on a standard Convolutional Neural Network (CNN) structure that has previously been successfully applied in particle detection and localization. The second, \PINRES, uses a Residual Neural Network (ResNet) architecture that is significantly deeper than the CNN while the third, \PINFPN{}, is based on a more advanced Feature Pyramid Network (FPN) that can take advantage of multi-scale information in an image. All networks are trained using the same collection of simulated data created with a range of SBRs and fluorescence emitter densities, as well as with three different Point Spread Functions (PSFs): a standard Born-Wolf model, a model for astigmatic imaging to allow localization in three dimensions, and a model of the Double-Helix engineered PSF. All PINs are evaluated and compared through data-intensive simulation and experiments under a variety of settings.
In the final contribution, we link all above together to create an algorithm that takes in raw camera data and produces trajectories and parameter estimates for multiple particles in an image sequence
