A well known result of rate-distortion theory states that, under broad conditions, the quantization error has a Gaussian distribution. It is also known that a Gaussian memoryless source is successively refinable. These results indicate that the use of code books designed for a generic Gaussian source for different stages of a residual vector quantizer does not result in loss of performance. In this work, we present a residual vector quantizer using an optimal (LBG) vector quantizer in the first stage and a Gaussian codebook in the other stages. The closeness of the distribution of the error signals to the Gaussian distribution is examined and it is shown that while the rate-distortion theoretic results are true only when the rate of the first stage is very high, in practice, even at moderate rates, the loss in the optimality is quite small.

A new method for indexing the points of a lattice-based vector quantizer (LBVQ) used to quantize the DCT coefficients of images is presented. With this method, a large number of lattice points can be selected as codewords. As a result, the quality of the compressed data can be very high. The problem is that the large number of points results in a high bit rate. To reduce the bit rate, a shorter representation is assigned to the more frequently used lattice points. These points are grouped and a prefix code is used to index these lattice points. Our method outperforms JPEG, particularly, in the case of images with high frequency components.