A Two-Dimensional Polynomial Filter

  • Authors:

  • A. N. Katulev;V. N. Kuznetsov;M. F. Malevinskii;G. M. Solomakha

  • Affiliations:

  • Tver State University, Tver, Russia;Tver State University, Tver, Russia;Tver State University, Tver, Russia;Tver State University, Tver, Russia

  • Venue:
  • Automation and Remote Control
  • Year:
  • 2003

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Abstract

The criterion of minimal variance of transformation error is applied to design an nth-order nonlinear polynomial filter for image processing under given moments of order up to 2n of the two-dimensional input signal and additive disturbance. Structurally, the filter is represented by Hammerstein kernels (weight functions) determined from the solution of a system of two-dimensional linear integral equations. For a linear filter, this system is reduced to a two-dimensional Wiener–Hopf equation. The filter accuracy is shown to increase with the filter order n (in any case, it does not decrease). The filter performance is illustrated for practical operation conditions of information transmission channels.