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Kathrin Bissantz, Nicolai Bissantz, Katharina Proksch

• The question whether structural changes in time-resolved images are of statistical significance or merely emerge from random noise is of great relevance in many practical applications such as live cell fluorescence microscopy, where intracellular diffusion processes are investigated. Using bootstrap-methods, we construct nonparametric confidence bands for time-resolved images from fluorescence microscopy and use these to detect and visualize temporal changes between individual frames in imaging of living cells. We model the images frames as two-dimensional fields of Poisson random variables and provide a strong approximation result for independent and standardized but not necessarily identically distributed Poisson random variables. The latter result is used to derive a limit result for the maximal difference between the reconstructed and the true image. This provides the theoretical foundation of our method. We apply regularization techniques to cope with the ill-posedness of the convolution problem induced by the imaging system. Our approach provides a criterion to assess time-resolved small scale structural changes, for example, in the nanometer range. It can also be adopted for use in other imaging systems. Moreover, a data-driven selection method for the regularization parameter based on statistical multiscale methods is discussed.