Optical EngineeringPartitioning of Hopfield networks and its application to image restoration
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Partitioning of Hopfield networks into submodules is important in large-scale problems for ease of implementation, say, with optical systems having limited space-bandwidth product. Two types of decomposition and their application to image restoration are discussed. In the case of two-stage partitioning, the system functions as a pair of Hopfield subnetworks that iteratively force the energy function to a minimum. The least-squares solution is attained by iteratively switching between the two networks until convergence. The algorithms are valid for any number of partitions. Partitioning also helps avoid the problem of possible limit cycles when threshold nonlinearities are used, and the problem of nonzero diagonal elements in the interconnection matrix when the partitions are implemented in parallel.