A compressed sensing approach to interpolation of fractional Brownian trajectories for a single particle tracking experiment

Abstract

In this paper, assuming that particles undergo the fractional Brownian motion, we propose the interpolation model based on the fact that the spectral density derived for the finite-length realization of this process obeys a power law decay. This allows us to apply the main idea of compressed sensing to reconstruct a given trajectory in the frequency domain. We conduct a simulation study with various trajectory degradation models reflecting typical limitations found in a single particle tracking experiment. Based on the statistical analysis we show that parameters characterizing the fractional Brownian motion estimated from trajectories interpolated by the proposed method are close to the ones estimated from the ground truth data.