A Two-Dimensional Polynomial Filter

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.