A New Design Method for Complex-Valued Multistate Hopfield Associative Memory

A method to store each element of an integer-valued memory set M ⊂ {1, 2,..., K}n as a fixed point into a complexvalued multistate Hopfield network is introduced. The method employs a set of inequalities to render each memory pattern as a strict local minimum of a quadratic energy landscape, and based on the solution of this system, gives a recurrent network of n multistate neurons with complex and symmetric synaptic weights, which operates on the finite state space {1, 2,..., K}n to minimize this quadratic functional. Maximum number of integer-valued vectors that can be embedded into the energy landscape of the network by this method is investigated by computer experiments. The paper also enlightens the performance of the proposed method in reconstructing noisy gray-scale images