A method for defining analog circuits for the minimization of discrete functionals: An image processing application

The solutions of many physical-mathematical problems can be obtained by min imizing proper functionals. In the literature, some methods for the synthes is of analog circuits (mainly cellular neural networks) are presented that find the solution of some of these problems by implementing the discretized Euler-Lagrange equations associated with the pertinent functionals. In this paper, we propose a method for defining analog circuits that direct ly minimize (in a parallel way) a class of discretized functionals in the f requently occurring case where the solution depends on two spatial variable s. The method is a generalization of the one presented in Parodi et al., In ternat. J. Circuit Theory AppL, 26, 477-498, 1998. The analog circuits cons ist of both a (nonlinear) resistive part and a set of linear capacitors, wh ose steady-state voltages represent the discrete solution to the problem. T he method is based on the potential (co-content) functions associated with voltage-controlled resistive elements. As an example, we describe an applic ation in the field of image processing: the restoration of color images cor rupted by additive noise.