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 minimizing proper functionals. In the literature, some methods for the synthesis 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 directly minimize (in a parallel way) a class of discretized functionals in the frequently occurring case where the solution depends on two spatial variables. The method is a generalization of the one presented in Parodi et al., Internat. J. Circuit Theory Appl., 26, 477-498, 1998. The analog circuits consist of both a (nonlinear) resistive part and a set of linear capacitors, whose steady-state voltages represent the discrete solution to the problem. The method is based on the potential (co-content) functions associated with voltage-controlled resistive elements. As an example, we describe an application in the field of image processing: the restoration of color images corrupted by additive noise.2