SE PhD Prospectus Defense of Ye Lin

TITLE: Joint Estimation of Trajectory and Model Parameters for Single Particle Tracking in Fluorescence Microscopy

ABSTRACT: Single Particle Tracking (SPT) plays an important role in studying physical and dynamic properties of biomolecules. 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. Our main goal is to develop mathematical tools to enhance the performance of localization and parameter estimation across a wide range of signal and noise levels. We also want to do this without needing to wait days to weeks for the algorithms to complete processing.

First, we demonstrate the motion and measurement models that well capture the dynamics of nanometer-scale biomolecules. Unlike the standard scheme that assumes a simple linear observation of the true particle position corrupted by additive white Gaussian noise, we consider more realistic measurements modeled as Poisson-distributed random variables with a rate that depends on the true location of the particle as well as on experimental realities, including background intensity noise and the details of the optics used in the instrument. Using such a detailed model is especially important at the low signal intensities that are often found in SPT data.

We then describe a generic Expectation Maximization (EM)-based framework for simultaneous localization and parameter estimation. 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 SMC method uses Particle Filtering (PF) and Particle Smoothing (PS) to handle general distributions, while the U approach uses an Unscented Kalman Filter (UKF) and an Unscented Rauch-Tung Striebel Smoother (URTSS).

We carry out a quantitative comparison among standard and EM-based SPT methods based on extensive simulations. Through a variety of physically realistic simulations, we find that both U-EM and SMC-EM have advantages over standard methods in the perspective of lo- calization and parameter estimation accuracy, and such advantages become more obvious as the signal level is decreasing. U-EM, while more computationally efficient than SMC-EM, is limited to slower diffusing speed, and cannot handle arbitrary distributions.

We then discuss the plan for future research work where the first stage is to extend the EM-based scheme to 3-D SPT scenarios, and the second stage is to utilize machine learning techniques to do automatic particle detection and image segmentation especially at low signal levels or high noise levels.

COMMITTEE: Advisor: Sean B. Andersson, SE, ME; Committee: David Castañón, SE, ECE; John Baillieul, SE, ME; Prakash Ishwar, SE, ECE