Pareto optimal nonlinear filters for image enhancement

A new method for a design of polynomial filters based on the Volterra series expansion is presented. The problem of nonlinear filter design is considered as a multi-objective problem and is solved by using an optimization approach. A theoretical background of the proposed method is stated. The obtained results allow one to design Pareto optimal filters in the presence of several conflicting criteria. In this case, the optimal nonlinear filter is characterized by a filter plane, which is tangent to a convex optimal decision function. The issue of reasonable choice of the design parameters defining the nonlinear filter performance is discussed. Examples of design, together with a performance comparison with other known nonlinear operators on simulated images, complete the article