A Compensated Fuzzy Hopfield Neural Network for Codebook Design in Vector Quantization

In this paper, a new Hopfield-model net called Compensated Fuzzy Hopfield Neural Network (CFHNN) is proposed for vector quantization in image compression. In CFHNN, the compensated fuzzy c-means algorithm, modified from penalized fuzzy cmeans, is embedded into Hopfield neural network so that the parallel implementation for codebook design is feasible. The vector quantization can be cast as an optimal problem that may also be regarded as a minimization of a criterion defined as a function of the average distortion between training vector and codevector. The CFHNN is trained to classify the divided vectors on a real image into feasible class to generate an available codebook when the defined energy function converges to near global minimum. The training vectors on a divided image are mapped to a two-dimensional Hopfield neural network. Also the compensated fuzzy c-means technique is used to update the quantization performance and to eliminate searching for the weighting factors. In the context of vector quantization, each training vector on the divided image is represented by a neuron which is fully connected by the other neurons. After a number of iterations, neuron states are refined to reach near optimal result when the defined energy function is converged.