In this paper, the application of an unsupervised parallel approach called the Fuzzy Hopfield Neural Network (FHNN) for vector qunatization in image compression is proposed. The main purpose is to embed fuzzy reasoning strategy into neural networks so that on-line learning and parallel implementation for codebook design are feasible. The object is to cast a clustering problem as a minimization process where the criterion for the optimum vector qunatization is chosen as the minimization of the average distortion between training vectors. In order to generate feasible results, a fuzzy reasoning strategy is included in the Hopfield neural network to eliminate the need of finding weighting factors in the energy function that is formulated and based on a basic concept commonly used in pattern classification, called the "within-class scatter matrix" principle. The suggested fuzzy reasoning strategy has been proven to allow the network to learn more effectively than the conventional Hopfield neural network. The FHNN based on the within-class scatter matrix shows the promising results in comparison with the c-means and fuzzy c-means algorithms.

In this paper color image compression using a fuzzy Hopfield-model net based on rough-set reasoning is created to generate optimal codebook based on Vector Quantization (VQ) in Discrete Wavelet Transform (DWT). The main purpose is to embed rough-set learning scheme into the fuzzy Hopfield network to construct a compression system named Rough Fuzzy Hopfield Net (RFHN). First a color image is decomposed into 3-D pyramid structure with various frequency bands. Then the RFHN is used to create different codebooks for various bands. The energy function of RFHN is defined as the upper- and lower-bound fuzzy membership grades between training samples and codevectors. Finally, near global-minimum codebooks in frequency domain can be obtained when the energy function converges to a stable state. Therefore, only 32/N pixels are selected as the training samples if a 3N-dimensional color image was used. In the simulation results, the proposed network not only reduces the consuming time but also preserves the compression performance.