Comunicazione
On a method for reconstructing potential fields with an application to superresolution microscopy.
Annunziato M., Borz`i A.
A method for the reconstruction of a potential field is presented. This method is based on the observation of stochastic trajectories of particles moving on the field subject to a drift given by the minus gradient of the potential and to a Brownian motion. The reconstruction technique is formulated as an inverse problem governed by the Fokker-Planck equation of the stochastic process and a best-fit functional with a Tikhonov regularization. This optimization problem is solved on a sequence of time windows, allowing to determine the potential together with an estimate of its uncertainty. An application is presented concerning the reconstruction of a cell membrane, based on data of superresolution microscopy of luminescent activated proteins.