Lyapunov function based design of dynamical neural networks for restoration of blurred and noisy images

In this paper, Hopfield network (HN) and cellular neural network (CNN) which are two special cases of first-order dynamical neural networks are applied for restoration of blurred and noisy images. It is known that maximum a posteriori (MAP) estimation based on regularized image restoration problems can be formulated as the minimization of the Lyapunov function of the discrete-time HN or its modified versions. This paper extends this Lyapunov function based design method used for the discrete-time HN in image restoration to the continuous-time CNN and to the continuous-time HN. Furthermore, it presents a simple solution to the convergence problem of the discrete-time HNs by adding an extra term to the cost function which yields zero or nonnegative self-feedback connection weights. A binary sum representation which requires eight binary neurons only for each image pixel is used for reducing computational costs. It is concluded that the considered continuous-time neural networks are suitable for real-time image restoration, and that the continuous-time CNN operating in the real valued steady-state output mode is best suited for the image restoration problem