Convex Relaxations for Particle-Gradient Flow with Applications in Super-Resolution Single-Molecule Localization Microscopy
Date of Award
Doctor of Philosophy (PhD)
Single-molecule localization microscopy (SMLM) techniques have become advanced bioanalytical tools by quantifying the positions and orientations of molecules in space and time at the nanoscale. With the noisy and heterogeneous nature of SMLM datasets in mind, we discuss leveraging particle-gradient flow 1) for quantifying the accuracy of localization algorithms with and without ground truth and 2) as a basis for novel, model-driven localization algorithms with empirically robust performance. Using experimental data, we demonstrate that overlapping images of molecules, a typical consequence of densely packed biological structures, cause biases in position estimates and reconstruction artifacts. To minimize such biases, we develop a novel sparse deconvolution algorithm by relaxing a particle-gradient flow algorithm (called relaxed-gradient flow or RGF). In contrast to previous methods based on sequential source matching or grid-based strategies, RGF detects source molecules based on the estimated “gradient flux.” RGF reconstructs experimental images of microtubules with much greater accuracy in terms of separation and diameter. We further extend RGF to the problem of joint estimation of molecular position and orientation. By lifting the optimization from first-order to second-order orientational moments, we derive an efficient version of RGF, which exhibits robustness to instrumental mismatches. Finally, we discuss the fundamental problem of quantifying the accuracy of a localization estimate without ground truth. We show that by computing measurement stability under a well-chosen perturbation with accurate knowledge of the imaging system, we can robustly quantify the confidence of individual localizations without ground-truth knowledge of the sample. To demonstrate the broad applicability of our method, termed Wasserstein-induced flux, we measure the accuracy of various reconstruction algorithms directly on experimental data.
Matthew D. Lew
Abhinav Kumar Jha, Ulugbek Kamilov, Arye Nehorai, Joseph O'Sullivan,