Conditional entropy coding of VQ indexes for image compression

Vector quantization (VQ) is a source coding methodology with provable rate-distortion optimality. However, despite more than two decades of intensive research, VQ theoretical promise is yet to be fully realized in image compression practice. Restricted by high VQ complexity in dimensions and due to high-order sample correlations in images, block sizes of practical VQ image coders are hardly large enough to achieve the rate-distortion optimality. Among the large number of VQ variants in the literature, a technique called address VQ (A-VQ) by Nasrabadi and Feng (1990) achieved the best rate-distortion performance so far to the best of our knowledge. The essence of A-VQ is to effectively increase VQ dimensions by a lossless coding of a group of 16-dimensional VQ codewords that are spatially adjacent. From a different perspective, we can consider a signal source that is coded by memoryless basic VQ to be just another signal source whose samples are the indices of the memoryless VQ codewords, and then induce the problem of lossless compression of the VQ-coded source. If the memoryless VQ is not rate-distortion optimal (often the case in practice), then there must exist hidden structures between the samples of VQ-coded source (VQ codewords). Therefore, an alternative way of approaching the rate-distortion optimality is to model and utilize these inter-codewords structures or correlations by context modeling and conditional entropy coding of VQ indexes.