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An algorithm is presented to calculate a state space realization of a 3D image set. It is based on interpreting the image set as the impulse response of a 3D separable system. As an application it is shown how the approximation steps, including balanced model reduction methods, in the algorithm can be used to suppress noise in 3D image sets. The approach was motivated by a practical problem in the analysis of 3D fluorescent microscopy image data of fluorescently labelled cells.