A Study of Particle Motion in the Presence of Clusters
Abstract
The motivation for this study came from the task of analysing the kinetic behavior of single molecules in a living cell based on Single Molecule Localization Microscopy. Given measurements of both the motion of clusters and molecules, the main task consists in detecting if a molecule belongs to a cluster. While the exact size of the clusters is usually unknown, upper bounds are available. In this study, we simulate the cluster movement by a Brownian motion and those of the particles by a Gaussian mixture model with two modes depending on the position of the particle within or outside a cluster. We propose various variational models to detect if a particle lies within a cluster based on the Wasserstein and maximum mean discrepancy distances between measures. We compare the performance of the proposed models for simulated data.
Keywords
Cite
@article{arxiv.2308.11314,
title = {A Study of Particle Motion in the Presence of Clusters},
author = {Christian Wald and Gabriele Steidl},
journal= {arXiv preprint arXiv:2308.11314},
year = {2023}
}