Despite superior performance of vector quantization (VQ) over scalar quantization in providing low bit rates at optimized distortion, the complexities involved in the encoding processes namely search processes and in generation of efficient code books in VQ prohibit the use of VQ in many applications. We introduce a new VQ technique with optimized search processes and distortion measures followed by entropy coding thereby yielding exceptionally low bit rates yet high visual quality for a large class of images including a variety of medical images with potential application in cost-effective telecommunications. A new approach to vector quantization by integrated self-organizing neural networks with fuzzy distortion measures has been applied to generate multiresolution codebooks from wavelet decomposed images. Two adaptive clustering techniques, namely integrated adaptive fuzzy clustering and adaptive fuzzy leader clustering with embedded fuzzy distortion measures, are used for partitioning similar vector groups for generating code books at each resolution level. The lower bound for the bits required to represent an image is given by its entropy. However, if the fundamental limit of compressing a signal can be related to perceptual entropy, then a bit rate lower than the entropy estimate can be achieved. The capability of this new approach to vector quantization resulting in low bit rate at high visual quality will have significant applications in telecommunications and telemedicine.