Parallel and distributed image restoration using a modified Hopfield network

A modified Hopfield network model for parallel and distributed image restoration is presented. The proposed network does not require the zero autoconnection assumption which is one of the major draw-backs of the original Hopfield network. A new number representation scheme is also given for implementation of the network. As a tool for the convergence analysis of parallel and distributed algorithms, the convergence of descent algorithms theorem is presented. According to this theorem, the proposed image restoration algorithm with sequential updates and decoupled parallel updates is shown to converge. The sufficient condition for convergence of n-simultaneous updates is also given. If this condition is satisfied, the algorithm with totally asynchronous updates is guaranteed to converge. When the image restoration problem does not satisfy the convergence condition, a greedy algorithm is used which guarantees convergence at the expense of image quality. The proposed algorithm with sequential updates performs identically to the algorithm using the original Hopfield network, without checking the reduction of the energy function at the update of each neuron.