In this talk we try to give a general introduction to statistical inverse problems, highlighting commonalities with deterministic inverse problems, specific difficulties, and important examples.   Afterwards we especially focus to deconvolution problems motivated by fluorescence microscopy. Here we present an algorithm, which is able to simultaneously segment an image obtained by a modified fluorescence microscope and to count the number of markers inside the segments while controling the uncertainty. Its performance is demonstrated in simulations and on experimental data.

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