State Space Realization of a Three-dimensional Image Set with Application to Noise Reduction of Fluorescent Microscopy Images of Cells

Abstract

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.

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Correspondence to Raimund J. Ober.

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Received July 9, 2003; Revised April 20, 2003; Accepted June 11, 2004; First online version published in December 2004

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Ober, R.J., Lai, X., Lin, Z. et al. State Space Realization of a Three-dimensional Image Set with Application to Noise Reduction of Fluorescent Microscopy Images of Cells. Multidim Syst Sign Process 16, 7–47 (2005). https://doi.org/10.1007/s11045-004-4737-0

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Keywords

  • multi-dimensional state space realization
  • separable n-D system
  • image processing
  • noise suppression
  • balanced realization
  • fluorescent microscopy