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.

The wavelet transform (WT) has recently emerged as a powerful tool for image compression. In this paper, a new image compression technique combining the genetic algorithm (GA) and grey-based competitive learning network (GCLN) in the wavelet transform domain is proposed. In the GCLN, the grey theory is applied to a two-layer modified competitive learning network in order to generate optimal solution for VQ. In accordance with the degree of similarity measure between training vectors and codevectors, the grey relational analysis is used to measure the relationship degree among them. The GA is used in an attempt to optimize a specified objective function related to vector quantizer design. The physical processes of competition, selection and reproduction operating in populations are adopted in combination with GCLN to produce a superior genetic grey-based competitive learning network (GGCLN) for codebook design in image compression. The experimental results show that a promising codebook can be obtained using the proposed GGCLN and GGCLN with wavelet decomposition.