Optimal vector transform for vector quantization

The vector transform has previously been proposed for vector quantization image coding. It is intended for decorrelating intervector dependency and preserving intravector dependency. The present authors study optimally such a transform. It is found that the optimal vector transform in the above senses, with the first-order Gaussian Markov model, does not exist unless the overall correlation matrix has an intervector and intravector decomposition structure. This is especially true for vectors formed by blocks of pixels. Then, a necessary and sufficient condition is derived for general vectors on the existence of their optimal vector transforms.<>