A computational method for the design of 2-D nonlinear Volterra filters

A class of nonlinear 2-D filters based on the truncated discrete Volterra series is considered, together with a suited matrix notation. An optimization method is developed for the design of the filters according to the required input/output relation. The performance of different optimization algorithms is studied, specifically, the method of steepest descent, Powell's conjugate directions algorithm, and simulated annealing. It is found that the Powell technique is the most suited to the problem. A design example, together with the results obtained after processing a test image by the proposed filters and other standard techniques, is used to compare the performance of the three methods. >