Vector quantization based on Gaussian mixture models

In this paper, we model the underlying probability density function of vectors in a database as a Gaussian mixture (GM) model. The model is employed for high rate vector quantization analysis and for design of vector quantizers. It is shown that the high rate formulas accurately predict the performance of model-based quantizers. We propose a novel method for optimizing GM model parameters for high rate performance, and an extension to the EM algorithm for densities having bounded support is also presented. The methods are applied to quantization of LPC parameters in speech coding and we present new high rate analysis results for band-limited spectral distortion and outlier statistics. In practical terms, we find that an optimal single-stage VQ can operate at approximately 3 bits less than a state-of-the-art LSF-based 2-split VQ.