Designing pareto optimal nonlinear filters for image processing

We consider a method of designing multidimensional polynomial filters characterized by an interval of a discrete functional Volterra series. This method allows designing Pareto optimal nonlinear filters by several criteria. We prove that finding a set of Pareto optimal alternatives is equivalent to minimizing a weighted target function. The designed nonlinear filter is characterized by the plane tangent to a convex optimal solving function, whose curvature is determined by how contradictory the given criteria are. We show examples of polynomial filter design for image processing and compare them with known filters of the same class.