State Space Realization of a Three-dimensional Image Set with Application to Noise Reduction of Fluorescent Microscopy Images of Cells
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A method is presented to calculate state space realizations of a three-dimensional 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 this method, combined with approximation steps, including balanced model reduction, can be used to suppress noise in three-dimensional image sets. The approach was motivated by a practical problem in the analysis of three-dimensional fluorescent microscopy image data of fluorescently labelled cells. The method is illustrated by an analysis of simulated data and experimental data. The proposed approach can also be applied to a two-dimensional image in a straightforward way.