Design of 2-Dimensional Recursive Filters
The design of two-dimensional (2-D) Recursive Filters,
within the field of digital signal processing, has been supported by optimization
techniques such as linear programming, Remez exchange algorithm, nonlinear
programming: gradient methods, direct search methods, Newton and Gauss–Newton
Methods, Fletcher–Powell, and conjugate gradient. Recent approaches also include
neural networks (NN) and genetic algorithms (GA).
A critical issue for any design methodology is to retain "stability conditions" represented as numerical constraints that specify a "stability region" within the search space. Most stochastic search methods—including genetic ones—perform tests within the search space, while penalize potential solutions not included in the stability region. However, consideration of the latter potential solutions reduce search efficiency, which is reflected in both computation time and solution quality.
Based on the expressive power of GENETICA we have developed an evolutionary design method where the stability region is defined to be closed with respect to the genetic operations. In particular the potential solutions have a uniform probability within the stability region and zero probability outside. This results in a focused, high efficiency search. The design method was implemented in the prototype version of GENETICA and tested on a design problem dealt with also by other NN and GA methods. Our method resulted in better solutions achieved in shorter computation time. Both the design method and the results are reported in:
I.F. Gonos, L.I. Virirakis, N.E. Mastorakis, M.N.S. Swamy, 2006. "Evolutionary Design of 2-Dimensional Recursive Filters via the Computer Language GENETICA", IEEE Transactions on Circuits and Systems—II: v.53, n.4.