An inverse problem approach to the probabilistic reconstruction of particle tracks on a censored and closed surface
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Investigation of dynamics processes in cell biology very often relies on the observation of sampled regions without considering re-entrance events. In the case of image-based observations of bacteria cell wall processes, a large amount of the cylinder-shaped wall is not observed. It follows that biomolecules may disappear for a period of time in a region of interest, and then reappear later. Assuming Brownian motion with drift, we address the mathematical problem of the connection of particle trajectories on a cylindrical surface. A subregion of the cylinder is typically observed during the observation period, and biomolecules may appear or disappear in any place of the 3D surface. procedure for trajectory reconnection. The performance of the method is mainly demonstrated on simulation data that mimic MreB dynamics observed in 2D time-lapse fluorescence microscopy.
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