Complex-Valued Multistate Associative Memory With Nonlinear Multilevel Functions for Gray-Level Image Reconstruction

A widely used complex-valued activation function for complex-valued multistate Hopfield networks is revealed to be essentially based on a multilevel step function. By replacing the multilevel step function with other multilevel characteristics, we present two alternative complex-valued activation functions. One is based on a multilevel sigmoid function, while the other on a characteristic of a multistate bifurcating neuron. Numerical experiments show that both modifications to the complex-valued activation function bring about improvements in network performance for a multistate associative memory. The advantage of the proposed networks over the complex-valued Hopfield networks with the multilevel step function is more outstanding when a complex-valued neuron represents a larger number of multivalued states. Further, the performance of the proposed networks in reconstructing noisy 256 gray-level images is demonstrated in comparison with other recent associative memories to clarify their advantages and disadvantages.