Redesigning vector quantizers using implicitly estimated probability density functions

Vector quantization is the most general form of quantization, and is a critical step in many compression systems for reducing the bitrate while controlling the distortion in the reconstructed signal. A vector quantizer (VQ) is usually designed using the generalized Lloyd algorithm which requires a training set that is assumed to be drawn from some underlying pdf characterizing the signal to be compressed. We consider here the problem of redesigning an existing VQ for some transformed or repartitioned signal space. Since VQ design is similar to the construction of nonlinear bin histograms, the VQ codebook provides an estimate of the pdf underlying the training set that was originally used to design it. We exploit this observation to synthesize training sets from the VQ codebooks such that they have statistics similar to those of the unknown original training sets. Using the proposed training set synthesis approach, we achieve improvements in performance of between 9.5% and 34% in VQ partitioning and redesign applications compared to a directly repartitioning and transforming the given VQ codebooks.