Approximation of an analog diffusion network with applications to image estimation

This work is concerned with a numerical procedure for approximating an anal og diffusion network. The key idea is to take advantage of the separable fe ature of the noise for the diffusion machine and use a parallel processing method to develop recursive algorithms. The asymptotic properties are studi ed. The main result of this paper is to establish the convergence of a cont inuous-time interpolation of the discrete-time algorithm to that of the ana log diffusion network via weak convergence methods. The parallel processing feature of the network makes it attractive for solving large-scale optimiz ation problems. Applications to image estimation are considered. Not only i s this algorithm useful for the image estimation problems, but it is widely applicable to many related optimization problems.